Projective invariants of almost C(λ)-manifolds.

Autor: Rustanov, Aligadzhi R., Polkina, Elena A., Kharitonova, Svetlana V.
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Zdroj: Annals of Global Analysis & Geometry; Mar2022, Vol. 61 Issue 2, p459-467, 9p
Abstrakt: The tensor of projective curvature of almost C (λ) -manifolds is researched in this paper. Five projective invariants of almost C (λ) -manifolds are taken as a base and classes of almost C (λ) -manifolds: P i , i =1, 2,..., 5 are obtained. Local characterization of these classes is given. The present paper proves the following results. The set of almost C (λ) -manifolds of class P 1 coincides with the set of almost C (λ) -manifolds of class P 2 ; the set of almost C (λ) -manifolds of class P 3 coincides with the set of almost C (λ) -manifolds of class P 4 . Almost C (λ) -manifolds of classes P 1 and P 5 are Einstein manifolds. An almost C (λ) -manifold of class P 4 is a manifold of pointwise constant Φ -holomorphic sectional curvature c = 2 λ . Local characterization of projectively flat almost C (λ) -manifold is presented as well as almost C (λ) -manifold with projective tensor, which is skew-symmetric on two first indexes. Also contact analogs of Gray's identities for tensor of projective curvature of almost contact metric manifolds are defined. Having taken these identities as a base projective Gray's classes is obtained: C P i , i =1, 2, 3. It is proved that almost C (λ) -manifolds are manifolds of C P 2 and C P 3 , an almost C (λ) -manifold of class C P 1 is manifold of class P 5 . [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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