Background
Vaisman, Izu was born on June 22, 1938 in Jassy, Romania. Son of Strul and Etla (David) Vaisman. arrived in Israel, 1976.
(The present work grew out of a study of the Maslov class ...)
The present work grew out of a study of the Maslov class (e. g. (37), which is a fundamental invariant in asymptotic analysis of partial differential equations of quantum physics. One of the many in terpretations of this class was given by F. Kamber and Ph. Tondeur (43, and it indicates that the Maslov class is a secondary characteristic class of a complex trivial vector bundle endowed with a real reduction of its structure group. (In the basic paper of V. I. Arnold about the Maslov class (2, it is also pointed out without details that the Maslov class is characteristic in the category of vector bundles mentioned pre viously. ) Accordingly, we wanted to study the whole range of secondary characteristic classes involved in this interpretation, and we gave a short description of the results in (83. It turned out that a complete exposition of this theory was rather lengthy, and, moreover, I felt that many potential readers would have to use a lot of scattered references in order to find the necessary information from either symplectic geometry or the theory of the secondary characteristic classes. On the otherhand, both these subjects are of a much larger interest in differential geome try and topology, and in the applications to physical theories.
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(Everybody having even the slightest interest in analytica...)
Everybody having even the slightest interest in analytical mechanics remembers having met there the Poisson bracket of two functions of 2n variables (pi, qi) f g ~(8f8g 8 8 ) (0.1) {f,g} = L...~ji - ji~ ,;=1 p, q q p, and the fundamental role it plays in that field. In modern works, this bracket is derived from a symplectic structure, and it appears as one of the main in- gredients of symplectic manifolds. In fact, it can even be taken as the defining clement of the structure (e.g., TIl). But, the study of some mechanical sys- tems, particularly systems with symmetry groups or constraints, may lead to more general Poisson brackets. Therefore, it was natural to define a mathematical structure where the notion of a Poisson bracket would be the primary notion of the theory, and, from this viewpoint, such a theory has been developed since the early 19708, by A. Lichnerowicz, A. Weinstein, and many other authors (see the references at the end of the book). But, it has been remarked by Weinstein We3 that, in fact, the theory can be traced back to S. Lie himself Lie.
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educator mathematics researcher
Vaisman, Izu was born on June 22, 1938 in Jassy, Romania. Son of Strul and Etla (David) Vaisman. arrived in Israel, 1976.
Master of Science in Mathematics, Jassy University, 1959. Doctor of Philosophy in Mathematics, Jassy University, 1965. Doctorate (honorary), Jassy University, 1999.
Assistant professor mathematics Jassy University, 1964-1969, associate professor mathematics, 1969-1976. Professor mathematics University Haifa, Israel, 1976—2006, professor emeritus, 2006. Chairman department mathematics, University Haifa, 1982-1984, 99-2001.
(Everybody having even the slightest interest in analytica...)
(The present work grew out of a study of the Maslov class ...)
Member Israel Mathematics Union.
Married Silvia Avram, May 8, 1969.