Abstract
References
- Alekseevsky, D. V., Cort´es, V. and Devchand, C. Special complex manifolds, J. Geom. Phys. 42(1-2), 85–105, 2002.
- Binh, T. Q. On semi-symmetric connections, Period. Math. Hungar. 21 (2), 101–107, 1990.
- Blaga, A. M. and Crasmareanu, M. The geometry of product conjugate connections, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 58 (2012), in press.
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- Cruceanu, V. Almost product bicomplex structures on manifolds, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 51 (1), 99–118, 2005.
- Gauduchon, P. Hermitian connections and Dirac operators, Boll. Un. Mat. Ital. B (7) 11 (2) suppl., 257–288, 1997.
- Hiric˘a, I. E. and Nicolescu, L. On quarter-symmetric metric connections on pseudo- Riemannian manifolds, Balkan J. Geom. Appl. 16 (1), 56–65, 2011.
- Ishihara, S. Quaternion K¨ahlerian manifolds, J. Diff. Geom. 9, 483–500, 1974.
- Kirichenko, V. F. Method of generalized Hermitian geometry in the theory of almost contact manifold, Itogi Nauki i Tekhniki, Problems of geometry 18, 25–71, 1986; translated in J. Soviet. Math. 42 (5), 1885–1919, 1988.
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- Phys. 57 (3), 999–1014, 2007.
Abstract
Properties of pairs of conjugate connections are stated with a special view towards the duality of these connections. We express the complex conjugate connections in terms of the structural and the virtual tensors from the almost complex geometry. For a pair of almost complex structures we discuss their mutual recurrence by pointing out that an almost quaternionic structure is implied. The notion of complex conjugate connections is extended in two directions, one called generalized obtained by adding a general (1, 2)-tensor field and the other called exponential since it involves the exponential of the almost complex structure considered.
Keywords
Almost complex structure (Conjugate) Linear connection Hermitian manifold Structural and virtual tensor field 2000 AMS Classification: 53 B 05
References
- Alekseevsky, D. V., Cort´es, V. and Devchand, C. Special complex manifolds, J. Geom. Phys. 42(1-2), 85–105, 2002.
- Binh, T. Q. On semi-symmetric connections, Period. Math. Hungar. 21 (2), 101–107, 1990.
- Blaga, A. M. and Crasmareanu, M. The geometry of product conjugate connections, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 58 (2012), in press.
- Calin, O., Matsuzoe, H. and Zhang, J. Generalizations of conjugate connections, in Trends in differential geometry, complex analysis and mathematical physics. Proceedings of 9th international workshop on complex structures, integrability and vector fields, Sofia, Bulgaria, August 25-29, 2008. (World Scientific, Hackensack NJ, 2009), 26–34.
- Cruceanu, V. Almost product bicomplex structures on manifolds, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 51 (1), 99–118, 2005.
- Gauduchon, P. Hermitian connections and Dirac operators, Boll. Un. Mat. Ital. B (7) 11 (2) suppl., 257–288, 1997.
- Hiric˘a, I. E. and Nicolescu, L. On quarter-symmetric metric connections on pseudo- Riemannian manifolds, Balkan J. Geom. Appl. 16 (1), 56–65, 2011.
- Ishihara, S. Quaternion K¨ahlerian manifolds, J. Diff. Geom. 9, 483–500, 1974.
- Kirichenko, V. F. Method of generalized Hermitian geometry in the theory of almost contact manifold, Itogi Nauki i Tekhniki, Problems of geometry 18, 25–71, 1986; translated in J. Soviet. Math. 42 (5), 1885–1919, 1988.
- Sch¨afer, L. tt*-geometry on the tangent bundle of an almost complex manifold, J. Geom.
- Phys. 57 (3), 999–1014, 2007.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | January 1, 2012 |
| Published in Issue | Year 2012 Volume: 41 Issue: 1 |