منابع مشابه
On totally umbilic submanifolds of semi-Riemannian manifolds
The notion of being totally umbilic is considered for non-degenerate and degenerate submanifolds of semi-Riemanian manifolds. After some remarks on the general case, timelike and lightlike totally umbilic submanifolds of Lorentzian manifolds are discussed, along with their physical interpretation in view of general relativity. In particular, the mathematical notion of totally umbilic submanifol...
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In literature (Kobayashi and Nomizu, 1963, 1969; Yano and Ako, 1972; Ishihara, 1974; Özdemir, 2006; Alagöz et al., 2012), almost complex and almost quaternionic structures have been investigated widely. These structures are special structures on the tangent bundle of a manifold. A detailed review can be found in Kirichenko and Arseneva (1997). Let us recall some basic facts and definitions from...
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We consider the basic heat operator on functions on a Riemannian foliation of a compact, Riemannian manifold, and we show that the trace KB(t) of this operator has a particular asymptotic expansion as t → 0. The coefficients of t and of t(log t) in this expansion are obtainable from local transverse geometric invariants functions computable by analyzing the manifold in an arbitrarily small neig...
متن کاملNoncommutative spectral geometry of Riemannian foliations
According to [9, 8], the initial datum of noncommutative differential geometry is a spectral triple (A,H, D) (see Section 3.1 for the definition), which provides a description of the corresponding geometrical space in terms of spectral data of geometrical operators on this space. The purpose of this paper is to construct spectral triples given by transversally elliptic operators with respect to...
متن کاملLightlike foliations of semi-Riemannian manifolds1
Using screen distributions and lightlike transversal vector bundles we develop a theory of degenerate foliations of semiRiemannian manifolds. We build lightlike foliations of a semiRiemannian manifold by suspension of a group homomorphism φ : π1(B, x0) → Isom(T ). We compute the basic cohomology groups of the flow determined by a lightlike Killing vector field on a complete semi-Riemannian mani...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1990
ISSN: 0026-2285
DOI: 10.1307/mmj/1029004072