### ON KENMOTSU MANIFOLDS

DOI QR Code

JUN JAE-BOK;DE UDAY CHAND;PATHAK GOUTAM

• 발행 : 2005.05.01
• 53 8

#### 초록

The purpose of this paper is to study a Kenmotsu manifold which is derived from the almost contact Riemannian manifold with some special conditions. In general, we have some relations about semi-symmetric, Ricci semi-symmetric or Weyl semisymmetric conditions in Riemannian manifolds. In this paper, we partially classify the Kenmotsu manifold and consider the manifold admitting a transformation which keeps Riemannian curvature tensor and Ricci tensor invariant.

#### 키워드

Ricci semi-symmetric Kenmotsu manifold;Weyl semisymmetric Kenmotsu manifold;$\eta$-Einstein manifold;$\eta$-parallel Ricci tensor

#### 참고문헌

1. K. Kenmotsu, A class of contact Riemannian manifold, Tohoku Math. Jour. 24 (1972), 93-103 https://doi.org/10.2748/tmj/1178241594
2. Z.I. Szabo, Structure theorem on Riemannian spaces satisfying R(X,Y) . R = 0, I. The local version, J. Differential Geom. 17 (1982), 531-582
3. L. Verstraelen, Comments on pseudo-symmetry in the sence of R. Deszcz, Geometry and Topology of submanifolds VI , World Scientific, 1933, 199-209
4. E.M. Patterson, Some theorems on Ricci recurrent spaces, J. London Math. Soc. 27 (1952), 287-295 https://doi.org/10.1112/jlms/s1-27.3.287
5. D.E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics 509, Springer-Verlag, Berlin, 1976
6. B. ONeil, Semi-Riemannian geometry with application to relativity, Academic Press, p. 208
7. M.C. Chaki and M. Tarafdar, On a type of Sasakian manifold, Soochow J. Math. 16 (1990), 23-28
8. T. Adati and T. Miyazawa, On a Riemannian space with recurrent conformal curvature, Tensor (N.S.) 18 (1967), 348-354
9. M. Kon, Invariant submanifolds in Sasakian manifolds, Math. Ann. 219 (1976), 277-290 https://doi.org/10.1007/BF01354288
10. S. Sasaki, Lecture notes on almost contact manifolds, Part II, Tohoku University, 1967

#### 피인용 문헌

1. 1. Locally Symmetric CR-Integrable Almost Kenmotsu Manifolds vol.12, pp.1, 2015, doi:10.4134/JKMS.2005.42.3.435
2. 2. On a type of almost Kenmotsu manifolds with nullity distributions vol.23, pp.2, 2017, doi:10.4134/JKMS.2005.42.3.435
3. 3. On invariant submanifolds of Kenmotsu manifolds vol.106, pp.1, 2015, doi:10.4134/JKMS.2005.42.3.435
4. 4. ON A SEMI-SYMMETRIC METRIC CONNECTION IN AN (ε)-KENMOTSU MANIFOLD vol.29, pp.2, 2014, doi:10.4134/JKMS.2005.42.3.435
5. 5. Some Curvature Properties of Kenmotsu Manifolds vol.85, pp.3, 2015, doi:10.4134/JKMS.2005.42.3.435
6. 6. On lightlike geometry in indefinite Kenmotsu manifolds vol.62, pp.2, 2012, doi:10.4134/JKMS.2005.42.3.435
7. 7. On Concircular Curvature Tensor with respect to the Semi-symmetric Non-metric Connection in a Kenmotsu Manifold vol.56, pp.3, 2016, doi:10.4134/JKMS.2005.42.3.435
8. 8. Ricci Semi-symmetric Hypersurfaces in Complex Two-Plane Grassmannians vol.40, pp.3, 2017, doi:10.4134/JKMS.2005.42.3.435