Results 1 - 10 of 4248
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[en] This letter presents a study of the automorphisms and the derivations of a large class of local Lie algebras over a manifold M (in the sense of Shiga and Kirillov) called Lie algebras of order O over M. It is shown that, in general, the algebraic structure of such an algebra GAMMA characterizes the differentiable structure of M and that the Lie algebra of derivations of GAMMA is a Lie algebra of differential operators of order 1 over M obtained in a natural way as the space of sections of a vector bundle canonically associated to GAMMA. (Auth.)
[en] A nearly Kaehler manifold is a special almost hermitian manifold. The geometry and topology of a nearly Kaehler manifold are studied. Contents: introduction; nearly Kaehler manifolds which are not Kaehler; sectional curvatures of a nearly Kaehler manifold; homotopy groups of a nearly Kaehler manifold; cohomology structure of a nearly Kaehler manifold; Chern classes of a nearly Kaehler manifold; submanifolds of a nearly Kaehler mainfold; nearly Kaehler structure in a local co-ordinate system. (author)
[en] A result of van de Ven is described which shows that there are topological obstructions to integrability for almost-complex structures on four-manifolds. A brief review is given of the salient definitions and properties and a theorem of Hirzebruch and Hopf is discussed which gives necessary and sufficient conditions for a compact, oriented four-manifold to have an almost-complex structure. (author)
[en] It is demonstrated that if C is a smooth curve of degree d>3g+3 in P3, the curve T of trisecants to C considered immerged in the variety C3 of divisors of 3 degree in C is connected. 7 refs
[en] For the function holomorphic in curved tubular domain the connection between asymptotic behaviour of real part of its boundary value at a given point of base manifold and asymptotic behaviour of the whole function from the inside of this domain is studied. (author). 3 refs
[en] This paper gives a survey of the index theory of tangentially elliptic and transversally elliptic operators on foliated manifolds as well as of related notions and results in non-commutative geometry.
[en] Presently, some confusions are made on the way of understanding the relation and the difference between the conformal flatness and the quasiumbilicity of submanifolds. The purpose of this paper is to make a clarification on these two topics: We review all the up-to-date known main results and the open related problems. (author). 18 refs
[en] The hypersurfaces of En+1 have been studied for the particular case when they satisfy the R.C-condition or the C.R-condition. One objective is to generalize this situation to a higher codimension. More precisely, we consider the case of dimension 4, and replace the condition of quasiumbilicity by the conformal flatness. In this way, we construct an example of 4-submanifold of IE6 which is conformally flat at a particular point without being quasiumbilical. That such submanifolds exist, was asserted without proof. Thus, we present another counter-example. (author). 4 refs
[en] A cohomological degree theory is constructed for continuous maps of topological manifolds, including manifolds with boundaries, with emphasis on the non-orientable case. Some applications are given, among which the most substantial is an extremely simple definition of Hopf's absolute degree (which coincides with the geometric degree). Bibliography: 29 titles.