A new curvature-like tensor in an almost contact Riemannian manifold
| dc.contributor.author | Koji Matsumoto | |
| dc.date.accessioned | 2018-12-19T12:53:33Z | |
| dc.date.available | 2018-12-19T12:53:33Z | |
| dc.date.issued | 2017 | |
| dc.description.abstract | In a M. Prvanović’s paper [5], we can find a new curvature-like tensor in an almost Hermitian manifold.In this paper, we define a new curvature-like tensor, named contact holomorphic Riemannian, briefly (CHR), curvature tensor in an almost contactRiemannian manifold. Then, using this tensor, we mainly research (CHR)-curvature tensor in a Kenmotsu and a Sasakian manifold. We introducethe flatness of a (CHR)-curvature tensor and show that a Kenmotsu anda Sasakian manifold with a flat (CHR)-curvature tensor is flat, see Theorems3.1 and 4.1. Next, we introduce the notion of an (CHR)-n-Einstein inan almost contact Riemannian manifold. In particular, in a Sasakian or aKenmotsu manifold, a (CHR)-n-Einstein manifold is n-Einstein, see Theorem5.3. Finally, from this tensor, we introduce a notion of a (CHR)-spaceform in an almost contact Riemannian manifold. In particular, if a Kenmotsuand a Sasakian manifold are (CHR)-space form, then the (CHR)-curvaturetensor satisfies a special equation, see Theorems 6.2 and 7.1. | |
| dc.identifier.issn | 2409-8906 | |
| dc.identifier.uri | https://card-file.ontu.edu.ua/handle/123456789/6219 | |
| dc.identifier.uri | https://doi.org/10.15673/tmgc.v9i3-4.320 | |
| dc.source | Proceedings of the International Geometry Center | |
| dc.title | A new curvature-like tensor in an almost contact Riemannian manifold |