Abstract
References
- [1] G. Ganchev and A. Borisov, Note on the almost complex manifolds with a Norden metric, Compt. Rend. Acad. Bulg. Sci. 39 (5), 31–34, 1986.
- [2] G. Ganchev, K. Gribachev and V. Mihova, B-connections and their conformal invari- ants on conformally Kähler manifolds with B-metric, Publ. Inst. Math. (Beograd) (N.S.) 42, 107–121, 1987.
- [3] G. Ganchev and V. Mihova, Canonical connection and the canonical conformal group on an almost complex manifold with B-metric, Ann. Univ. Sofia Fac. Math. Inform. 81 (1), 195–206, 1987.
- [4] K.I. Gribachev, D.G. Mekerov and G.D. Djelepov, Generalized B-manifolds, Compt. Rend. Acad. Bulg. Sci. 38 (3), 299–302, 1985.
- [5] H.A. Hayden, Sub-spaces of a space with torsion, Proc. London Math. Soc. S2-34, 27–50, 1932.
- [6] M. Iscan and A.A. Salimov, On Kähler-Norden manifolds, Proc. Indian Acad. Sci. (Math. Sci.), 119 (1), 71–80, 2009.
- [7] M. Manev, On canonical-type connections on almost contact complex Riemannian manifolds, Filomat, 29 (3), 411–425, 2015.
- [8] A. Salimov, Tensor operators and their applications, (Mathematics Research Devel- opments Series), Nova Science Publ., New York, 2013.
- [9] S. Tachibana, Analytic tensor and its generalization, Tohoku Math. J. 12, 208–221, 1960.
- [10] K. Yano, On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl. 15, 1579–1586, 1970.
- [11] K. Yano and M. Ako, On certain operators associated with tensor fields, Kodai Math. Sem. Rep. 20, 414–436, 1968.
- [12] K. Yano and T. Imai, On semi-symmetric metric F- connection, Tensor (N.S.) 29 (2), 134–138, 1975.
Abstract
In this paper, we construct a complex semi-symmetric metric $F$-connection on an anti-Kähler manifold. First, we present some results concerning the torsion tensor of the complex semi-symmetric metric $F$-connection. Finally, we find expressions of the curvature tensor, the conharmonic curvature tensor and the Weyl projective curvature tensor of such connection, and study their properties.
Keywords
pure tensor anti-Kähler manifold complex semi-symmetric metric $F$-connection curvature tensor Tachibana operator
References
- [1] G. Ganchev and A. Borisov, Note on the almost complex manifolds with a Norden metric, Compt. Rend. Acad. Bulg. Sci. 39 (5), 31–34, 1986.
- [2] G. Ganchev, K. Gribachev and V. Mihova, B-connections and their conformal invari- ants on conformally Kähler manifolds with B-metric, Publ. Inst. Math. (Beograd) (N.S.) 42, 107–121, 1987.
- [3] G. Ganchev and V. Mihova, Canonical connection and the canonical conformal group on an almost complex manifold with B-metric, Ann. Univ. Sofia Fac. Math. Inform. 81 (1), 195–206, 1987.
- [4] K.I. Gribachev, D.G. Mekerov and G.D. Djelepov, Generalized B-manifolds, Compt. Rend. Acad. Bulg. Sci. 38 (3), 299–302, 1985.
- [5] H.A. Hayden, Sub-spaces of a space with torsion, Proc. London Math. Soc. S2-34, 27–50, 1932.
- [6] M. Iscan and A.A. Salimov, On Kähler-Norden manifolds, Proc. Indian Acad. Sci. (Math. Sci.), 119 (1), 71–80, 2009.
- [7] M. Manev, On canonical-type connections on almost contact complex Riemannian manifolds, Filomat, 29 (3), 411–425, 2015.
- [8] A. Salimov, Tensor operators and their applications, (Mathematics Research Devel- opments Series), Nova Science Publ., New York, 2013.
- [9] S. Tachibana, Analytic tensor and its generalization, Tohoku Math. J. 12, 208–221, 1960.
- [10] K. Yano, On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl. 15, 1579–1586, 1970.
- [11] K. Yano and M. Ako, On certain operators associated with tensor fields, Kodai Math. Sem. Rep. 20, 414–436, 1968.
- [12] K. Yano and T. Imai, On semi-symmetric metric F- connection, Tensor (N.S.) 29 (2), 134–138, 1975.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | June 2, 2020 |
| Published in Issue | Year 2020 Volume: 49 Issue: 3 |