A new curvature-like tensor in an almost contact Riemannian manifold
<p><span>In a M. Prvanović’s paper [5], we can find a new curvature-like tensor in an almost Hermitian manifold.</span><br /><span>In this paper, we define a new curvature-like tensor, named contact holomorphic Riemannian, briefly (CHR), curvature tensor in an almost co...
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| Format: | Article |
| Language: | English |
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Odesa National University of Technology
2016-12-01
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| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
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| Online Access: | http://journals.gsjp.eu/index.php/geometry/article/view/320 |
| Summary: | <p><span>In a M. Prvanović’s paper [5], we can find a new curvature-like tensor in an almost Hermitian manifold.</span><br /><span>In this paper, we define a new curvature-like tensor, named contact holomorphic Riemannian, briefly (CHR), curvature tensor in an almost contact</span><br /><span>Riemannian manifold. Then, using this tensor, we mainly research (CHR)-</span><br /><span>curvature tensor in a Kenmotsu and a Sasakian manifold. We introduce</span><br /><span>the flatness of a (CHR)-curvature tensor and show that a Kenmotsu and</span><br /><span>a Sasakian manifold with a flat (CHR)-curvature tensor is flat, see Theorems</span><br /><span>3.1 and 4.1. Next, we introduce the notion of an (CHR)-<em>n</em>-Einstein in</span><br /><span>an almost contact Riemannian manifold. In particular, in a Sasakian or a</span><br /><span>Kenmotsu manifold, a (CHR)-<em>n</em>-Einstein manifold is <em>n</em>-Einstein, see Theorem</span><br /><span>5.3. Finally, from this tensor, we introduce a notion of a (CHR)-space</span><br /><span>form in an almost contact Riemannian manifold. In particular, if a Kenmotsu</span><br /><span>and a Sasakian manifold are (CHR)-space form, then the (CHR)-curvature</span><br /><span>tensor satisfies a special equation, see Theorems 6.2 and 7.1.</span></p> |
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| ISSN: | 2072-9812 2409-8906 |