×

Structures on generalized Sasakian-space-forms. (English) Zbl 1156.53027

Summary: Contact metric and trans-Sasakian generalized Sasakian-space-forms are deeply studied. We present some general results for manifolds with dimension greater than or equal to 5, and we also pay a special attention to the 3-dimensional cases.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53D15 Almost contact and almost symplectic manifolds
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Alegre, P.; Blair, D.E.; Carriazo, A., Generalized Sasakian-space-forms, Israel J. math., 141, 157-183, (2004) · Zbl 1064.53026
[2] P. Alegre, A. Carriazo, Generalized Sasakian-space-forms and conformal changes of metric, Preprint · Zbl 1219.53048
[3] P. Alegre, A. Carriazo, C. Özgür, S. Sular, New examples of generalized Sasakian-space-forms, Preprint · Zbl 1176.53047
[4] Blair, D.E., Riemannian geometry of contact and symplectic manifolds, (2002), Birkhäuser Boston · Zbl 1011.53001
[5] Blair, D.E.; Koufogiorgos, T.; Papantoniou, B.J., Contact metric manifolds satisfying a nullity condition, Israel J. math., 91, 189-214, (1995) · Zbl 0837.53038
[6] Blair, D.E.; Koufogiorgos, T.; Sharma, R., A classification of 3-dimensional contact metric manifolds with \(Q \varphi = \varphi Q\), Kodai math. J., 13, 391-401, (1990) · Zbl 0716.53041
[7] Boeckx, E., A full classification of contact metric \((k, \mu)\)-spaces, Illinois J. math., 44/1, 212-219, (2000) · Zbl 0969.53019
[8] Bueken, P.; Vanhecke, L., Curvature characterizations in contact geometry, Riv. mat. univ. parma (4), 14, 303-313, (1988) · Zbl 0689.53021
[9] Cabrerizo, J.L.; Carriazo, A.; Fernández, L.M.; Fernández, M., Slant submanifolds in Sasakian manifolds, Glasgow math. J., 42, 125-138, (2000) · Zbl 0957.53022
[10] Cabrerizo, J.L.; Carriazo, A.; Fernández, L.M.; Fernández, M., Structure on a slant submanifold of a contact manifold, Indian J. pure appl. math., 31, 857-864, (2000) · Zbl 0984.53034
[11] De, U.C.; Tripathi, M.M., Ricci tensor in 3-dimensional trans-Sasakian manifolds, Kyungpook math. J., 43, 247-255, (2003) · Zbl 1073.53060
[12] Kenmotsu, K., A class of almost contact Riemannian manifolds, Tôhoku math. J., 24, 93-103, (1972) · Zbl 0245.53040
[13] Koufogiorgos, T.; Tsichlias, C., On the existence of a new class of contact metric manifolds, Canad. math. bull., 43/4, 440-447, (2000) · Zbl 0978.53086
[14] Marrero, J.C., The local structure of trans-Sasakian manifolds, Ann. mat. pura appl., 162, 77-86, (1992) · Zbl 0772.53036
[15] Oubiña, J.A., New classes of almost contact metric structures, Publ. math. debrecen, 32, 187-193, (1985) · Zbl 0611.53032
[16] Sharma, R., On the curvature of contact metric manifolds, J. geometry, 53, 179-190, (1995) · Zbl 0833.53033
[17] Tricerri, F.; Vanhecke, L., Curvature tensors on almost Hermitian manifolds, Trans. amer. math. soc., 267, 365-398, (1981) · Zbl 0484.53014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.