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Turkish Journal of Mathematics

Author ORCID Identifier

ALIGADZHI RUSTANOV: 0000-0001-5217-8167

SVETLANA KHARITONOVA: 0000-0002-7670-7921

Abstract

Conformally flat harmonic nearly trans-Sasakian manifolds are studied. In the space of adjoint G-structure, components of the Weyl tensor of the conformal curvature are calculated, identities for this tensor are found, and also some conformal invariants of harmonic nearly trans-Sasakian manifold are provided. An exhaustive description of the class W1 of such manifolds is obtained. It is proved that this class is locally equivalent to the product of a complex Euclidean space and a real line. Complete local characteristic of harmonic nearly trans-Sasakian manifolds of the class W6, which are Einstein manifolds, is obtained. Full classification of conformally flat harmonic nearly trans-Sasakian manifolds is given. In particular, it is proved that a conformally flat harmonic nearly trans-Sasakian manifold is either a space of constant negative curvature, or an image of the product of a six-dimensional sphere, equipped with a Kahler structure, and a real line under the canonical concircular transformation. Conformally flat harmonic nearly trans-Sasakian manifold of characteristic zero is locally equivalent to the product of a complex Euclidean space Cn equipped with the standard Hermitian metric and the real line R.

DOI

10.55730/1300-0098.3590

Keywords

closely cosymplectic structure, conformal curvature tensor, Harmomic nearly trans-Sasakian manifold

First Page

300

Last Page

311

Publisher

The Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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