Prof. Oldrich Kowalski

Prof. RNDr. Oldrich Kowalski, DrSc. Curiculum vitae:

Born 19. 6. 1936 in Brno, Czechoslovakia, 1954-59 study of Mathematics on the Faculty of Science, University in Brno. The degree “Candidate of Sciences” CSc (equivalent to PhD) in 1963. Habilitation in 1967, Faculty of Science, Brno. Highest scientific degree DrSc in 1983 - Mathematical Institute of the Academy. Nomination - full Professorship in 1991 on the Faculty of Mathematics and Physics, Charles University in Prague (further “MFF UK”) in Mathematics - Geometry and Topology

Personal data: included in all major encyclopedias which appeared in Czech Republic since 1992 (Who is who in Czech Republic, Czechoslovak Biographical Dictionary, Encyclopedia Diderot, etc.). Also available on all major (international electronic) information retrievers. Personal Web-page: www.karlin.mff.cuni.cz/~kowalski/.

Distinctions and awards:

1978 - faculty medal of 2nd degree, 1996 - faculty medal of 1st degree (MFF UK).

In 1998 elected ordinary member of the Czech Learned Society (equivalent to various “Academies” in European countries).

In 2001 silver medal of the Silesian University in Opava, 2002 awarded honorary title “Professor Emeritus” by the Rector.

Professional Carrier: 1959-63 Instructor, 1963-67 Assistant Professor, 1968-69 Associate Professor on the Faculty of Construction, Technical University in Brno. 1967-68 lecturer at Military Technical College in Cairo–Egypt (lectures for the branch of high school teachers). 1970-91 Associate Professor of Mathematics on MFF UK. 1973-76 Vice-Dean for scientific affairs on MFF UK, 1977-90 coordinator of the national research program “Geometric structures”. 1992-2001 Professor of Mathematics on MFF UK, since 2001 “Professor Emeritus of the Charles University” with part-time job. 1990-2001 member of the Scientific Council of MFF UK, since 2001 honorary member. Since 1991 member/vice-chairman of the national committee for defense of DrSc-degrees in geometry and topology, since 2004 (member) in the field “Mathematical Structures”.

Other activities in the professional community: Since 1970 up to now member of the central board of the Union of Czech Mathematicians and Physicists (JCMF); until 2001 Editor-in-Chief of the Union’s journal. Since 1991 member of the workgroup for Mathematics and Computer science of the Accrediting committee of the Czech Government (for higher education). 1992-98 member of the committee 201 (mathematics and computer science) of the Grant Agency of Czech Republic. 2000-03 member of the supervising committee of the Grant Agency of the Charles University.

Organizer or co-organizer of international conferences “Differential Geometry and Applications” (8x). Member of the program committees of major international conferences abroad (Bulgaria, Hungary, Italy, Spain).

Research activities: The main topic is differential geometry and particularly Riemannian geometry.

Selected results from the earlier period: Generalized symmetric spaces - in a series of papers the general theory of these spaces was developed and it was later summarized and completed in the unique existing (and frequently cited) monograph; differential operators on Riemannian manifolds and the converse of a Gelfand‘s theorem (jointly with L. Vanhecke); a classification of naturally reductive and commutative spaces in small dimensions (jointly with L. Vanhecke); the classification of D‘Atri spaces in dimension three (very frequently cited paper; volumes of tubes in Riemannian geometry (generalization of some results by H.Weyl from the Euclidean case to the general Riemannian case - jointly with L. Vanhecke. Classification of invariant Einstein metrics on Aloff-Wallach spaces (a paper with prestigious citations) - jointly with Z. Vlášek; solution of global extrinsic version of the so-called Volume Conjecture by A. Gray and L. Vanhecke about the volume of geodesic balls using the methods of geometric measure theory (jointly with D. Preiss); introduction of the notion of additive volume invariant and its application on the Volume Conjecture by Gray and Vanhecke (published in Acta Math-Djursholm). Explicit classification (in the form of a finite formula) of so-called non-elliptic semi-symmetric spaces (satisfying the identity R(X,Y)·R = 0) and further generalization of these results in collaboration with M. Sekizawa. Complete classification of curvature homogeneous spaces in dimension 3 (partially joint work with Z. Vlášek), study of homogeneous geodesics on homogeneous Riemannian manifolds (existence theorems), classification of g.o. spaces (Riemannian manifolds whose all geodesics are homogeneous) in dimension up to 7 (partially joint work with Z. Dušek), classification of homogeneous affine connections in dimension 2 (jointly with Z. Vlášek).

Member of the editorial boards of research journals: Since 2002 Editor-in-Chief of the journal Differential Geometry and its Applications (Elsevier, included in SCI). Since 1976 - Comment Math. Univ. Carolinae, since 1983 Annals of Global Analysis and Geometry (Kluwer, included in SCI), since 1991 Archivum Math. (MU Brno), 1997 Note di Matematica (Lecce, Italy).

Major invitations abroad: invited professor at the University of Leuven, Belgium (repeatedly), further invited professor on the universities in Torino, Florence and Lecce (repeatedly), invited speaker at the “Special Year in Geometry and Topology” (Maryland 1974), professor of category C4 at University of Leipzig (1993) and many other invitations to lectures (Paris, Bonn, Berlin-West, Bilbao, Santiago de Compostela etc.). 1992, 1995 and 2000 invitations to Japan for 1 month, totally about 25 lectures at Japanese universities, in 1995 invited speaker at the Annual Meeting of the Mathematical Society of Japan. A permanent invitation to the Geometrie-Tagung in Oberwolfach since 1973 till 1994. Several invitations to plenary lectures at major conferences abroad. Also, on official basis, many visits and lectures in the former USSR and GDR, Poland and Hungary.

Professional guidance: 10 graduate students (one from Belgium, one from Spain), 5 mathematicians for long-term research stays from Poland, Germany, Japan (for 2 years) and Russia - mostly in the 80-ies.

Responsible for the grant projects:

1993-1995 GA CR 201/93/0469, Geometry of Riemannian spaces and its applications to mechanics and robotics.

1996-1998 GA CR 201/96/0227, Geometry of Riemannian and pseudo-Riemannian spaces and

its applications to mechanics and robotics.

1999-2001 GA CR 201/99/0265, Computer-aided differential geometry and its applications to robotics.

2002-2004 GA CR 201/02/0616, Computer-aided research in Differential geometry and Applications.

Since 2005: GA CR 201/05/2707, Computer-aided Ruiemannian and affine geometry

Publication activity: 132 research publications including 4 monographs:

1) Generalized Symmetric Spaces (Lecture Notes in Math. 805, Springer 1980; Russian edition - MIR, Moscow 1984).

2) Elemente der Analysis on Mannigfaltigkeiten (Teubner-Texte zur Mathematik, Band 39, 1981)

3) Riemannian manifolds of conullity two (jointly with E. Boeckx and L. Vanhecke, World Scientific, 1996).

4) Japanese edition of the Czech text-book, Introduction to Riemannian Geometry. (Nippon Hyoronsha Publishers, 2001).

About 550 citations on “ISI Web of Science” - with few exceptions by foreign authors. 70 other publications (text-books, popularization articles, translations from English, German and Russian).

Main publications in the last seven years:

K1. O. Kowalski, S.Ž. Nikcevic: On geodesic graphs of Riemannian g.o. spaces. Archiv der Math. 73 (1999), 223-234. (Impact Factor 0.326)

K2. O. Kowalski, B. Opozda, Z. Vlášek: A Classification of Locally Homogeneous Affine Connections with Skew-Symmetric Ricci Tensor on 2-Dimensional manifolds. Monatsh. Math. 130 (2000), 109-125. (IF 0.504)

K3. O. Kowalski, M. Sekizawa: On Tangent Sphere Bundles with Small or Large Constant Radius.

Ann. Global. Anal. Geom.18 (2000) (special issue dedicated to A. Gray), 207-219. (IF

0.471)

K4. Z. Dušek, O. Kowalski: Geodesic graphs on the 13-dimensional group of Heisenberg type.

Math. Nachrichten 254-255 (2003), 87-96. (IF 0.388)

K5. G. Calvaruso, O. Kowalski, R. Marinosci: Homogeneous geodesics in solvable Lie groups.

Acta Math. Hungarica 101 (4) (2003), 313-322. (IF 0.268)

K6. O. Kowalski, B. Opozda, Z. Vlášek: On locally nonhomogeneous pseudo-Riemannian manifolds with locally homogeneous Levi-Civita connections. International J. Math. 14, 6 (2003), 1-14. (IF 0.514)

K7. O. Kowalski, B. Opozda, Z. Vlášek: A classification of locally homogenous connections on 2-dimensional manifolds via group-theoretical approach. Central European J. Math. 2 (1) (2004), 87-102.

K8. Z.Dušek, O.Kowalski, S.Ž.Nikcevic: New examples of g.o. spaces in dimension 7.

Differential Geometry and its Applications, 21, 1 (2004), 65-78. (IF 0.418)

K9. M.T.K. Abbassi and O. Kowalski: On g-natural metrics with constant scalar curvature on

unit tangent sphere bundle. In: Topics in Almost Hermitian Geometry and Related Fields,

Proceedings in honor of K. Sekigawa's 60th birthday, World Scientific, 2005, pp.1-29.

K10. O.Kowalski, Z.Vlášek: On 3D-manifolds with prescribed Ricci eigenvalues. In: Complex,

Contact and Symmetric Manifolds - In Honor of L. Vanhecke. Progress in Mathematics, Vol.

234, Birkhäuser Boston- Basel-Berlin, pp.187-208 (2005).

Papers in print:

O. Kowalski Z. Dušek
On lightlike homogeneous geodesics and the Geodesic Lemma for any signature
To appear in Publicationes Mathematicae Debrecen

O. Kowalski Z. Dušek
Geodesic graphs on special 7-dimensional g.o. manifolds
To appear in Rendiconti Circ. Mat. Palermo, Suppl., 2006

O. Kowalski Z. Dušek
Examples of pseudo-Riemannian g.o. manifolds
Proceedings of the Eighth International Conference on Geometry, Integrability and Quantization, ed. I.M.Mladenov, Manuel de León, SOFTEX Sofia, Sofia, 2006

O. Kowalski, S. Homolya
Simply connected two-step homogeneous nilmanifolds
To appear in Note di Matematica (Lecce)

O. Kowalski, M. Sekizawa
On the geometry of orthonormal frame bundles.
To appear in Mathematische Nachrichten

O. Kowalski, Z. Vlášek
Classification of locally projectively homogeneous torsion-less affine connections in the plane domains
To appear in Beiträge zur Algebra und Geometrie