Abstract
We investigate L-sectional curvature of S-manifolds with respect to the Riemannian connection and to certain semi-symmetric metric and non- metric connections naturally related with the structure, obtaining conditions for them to be constant and giving examples of S-manifolds in such conditions. Moreover, we calculate the scalar curvature in all the cases.
Keywords
S-manifold Semi-Symmetric Metric Connection Semi-Symmetric non-Metric Connection L-Sectional Curvature Scalar Curvature
References
- [1] M. Akif Akyol, A. Turgut Vanli and L.M. Fernandez, Curvature properties of a semi-symmetric metric connection de ned on S-manifolds, Ann. Polonici Math., Vol:107, No.1 (2013), 71-86.
- [2] M. Akif Akyol, A. Turgut Vanli and L.M. Fernandez, Semi-symmetry properties of S-manifolds endowed with a semi-symmetric non metric connection, to appear in An. Sti. Univ. \Al. I. Cuza" (Iasi) (2015).
- [3] D.E. Blair, Geometry of manifolds with structural group U(n)O(s), J. Di er. Geom., Vol:4 (1970), 155-167.
- [4] D.E. Blair, On a generalization of the Hopf bration, An. Sti. Univ. \Al. I. Cuza" (Iasi), Vol:17 (1971), 171-177.
- [5] D.E. Blair and G.D. Ludden, Hypersurfaces in almost contact manifolds, T^ohoku Math. J., Vol:21 (1969), 354-362.
- [6] J.L. Cabrerizo, L.M. Fernandez and M. Fernandez, The curvature tensor elds on f-manifolds with complemented frames, An. Sti. Univ. \Al. I. Cuza" (Iasi), Vol:36 (1990), 151-161.
- [7] A. Friedmann and J.A. Schouten, Uber die Geometrie der halbsymmetrischen Ubertragung, Math. Zeitschr., Vol:21 (1924), 211-223.
- [8] S.I. Goldberg and K.Yano, Globally framed f-manifolds, Illinois J. Math., Vol:15 (1971), 456-474.
- [9] S.I. Goldberg and K.Yano, On normal globally framed manifolds, T^ohoku Math. J., Vol:22 (1970), 362-370.
- [10] I. Hasegawa, Y. Okuyama and T. Abe, On p-th Sasakian manifolds, J. Hokkaido Univ. of Education (Section II A), Vol:37 (1986), 1-16.
- [11] H.A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc., Vol 34 (1932), 27-50.
- [12] M. Kobayashi and S. Tsuchiya, Invariant submanifolds of an f-manifold with complemented frames, Kodai Math. Sem. Rep., Vol:24 (1972), 430-450.
- [13] K. Yano, On a structure de ned by a tensor eld f of type (1,1) satisfying f3 + f = 0, Tensor, N. S., Vol:14 (1963), 99-109.
Abstract
References
- [1] M. Akif Akyol, A. Turgut Vanli and L.M. Fernandez, Curvature properties of a semi-symmetric metric connection de ned on S-manifolds, Ann. Polonici Math., Vol:107, No.1 (2013), 71-86.
- [2] M. Akif Akyol, A. Turgut Vanli and L.M. Fernandez, Semi-symmetry properties of S-manifolds endowed with a semi-symmetric non metric connection, to appear in An. Sti. Univ. \Al. I. Cuza" (Iasi) (2015).
- [3] D.E. Blair, Geometry of manifolds with structural group U(n)O(s), J. Di er. Geom., Vol:4 (1970), 155-167.
- [4] D.E. Blair, On a generalization of the Hopf bration, An. Sti. Univ. \Al. I. Cuza" (Iasi), Vol:17 (1971), 171-177.
- [5] D.E. Blair and G.D. Ludden, Hypersurfaces in almost contact manifolds, T^ohoku Math. J., Vol:21 (1969), 354-362.
- [6] J.L. Cabrerizo, L.M. Fernandez and M. Fernandez, The curvature tensor elds on f-manifolds with complemented frames, An. Sti. Univ. \Al. I. Cuza" (Iasi), Vol:36 (1990), 151-161.
- [7] A. Friedmann and J.A. Schouten, Uber die Geometrie der halbsymmetrischen Ubertragung, Math. Zeitschr., Vol:21 (1924), 211-223.
- [8] S.I. Goldberg and K.Yano, Globally framed f-manifolds, Illinois J. Math., Vol:15 (1971), 456-474.
- [9] S.I. Goldberg and K.Yano, On normal globally framed manifolds, T^ohoku Math. J., Vol:22 (1970), 362-370.
- [10] I. Hasegawa, Y. Okuyama and T. Abe, On p-th Sasakian manifolds, J. Hokkaido Univ. of Education (Section II A), Vol:37 (1986), 1-16.
- [11] H.A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc., Vol 34 (1932), 27-50.
- [12] M. Kobayashi and S. Tsuchiya, Invariant submanifolds of an f-manifold with complemented frames, Kodai Math. Sem. Rep., Vol:24 (1972), 430-450.
- [13] K. Yano, On a structure de ned by a tensor eld f of type (1,1) satisfying f3 + f = 0, Tensor, N. S., Vol:14 (1963), 99-109.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Article |
| Authors | |
| Submission Date | July 10, 2014 |
| Publication Date | April 1, 2016 |
| Published in Issue | Year 2016 Volume: 4 Issue: 1 |
Cite
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.