S-Manifolds Versus Indefinite S-Manifolds and Local Decomposition Theorems

Year 2016, , 1 - 8, 30.04.2016

Letizia Brunetti Anna Maria Pastore

https://doi.org/10.36890/iejg.591878

Cited By: 2

Abstract

To any globally framed f-manifold carrying a structure of S-manifold we associate several

indefinite S-manifolds. We determine the links between the corresponding Levi-Civita

connections and sectional curvatures. We state some local semi-Riemannian decomposition

theorems.

Keywords

Semi-Riemannian manifolds, indefinite metrics, Lorentz metrics, f-structures

References

• [1] Bejancu, Aurel and Farran, Hani Reda, Foliations and Geometric Structures, Springer Verlag, Berlin, 2006.
• [2] Blair, D.E., Geometry of manifolds with structural group U (n) × O(s), J. Differential Geometry 4 (1970), 155–167.
• [3] Blair, D.E., Riemannian geometry of contact and symplectic manifolds, Progr. Math., 203, Birkhäuser Boston, Boston, MA, 2002.
• [4] Brunetti, L. and Pastore, A.M., Curvature of a class of indefinite globally framed f -manifolds, Bull. Math. Soc. Sci. Math. Roumanie 51 99 (2008), no.3, 183–204.
• [5] Brunetti, L. and Pastore, A.M., Examples of indefinite globally framed f -structures on compact Lie groups, Publ. Math. Debrecen 80 1-2 (2012), 215–234.
• [6] Brunetti, L. and Pastore, A.M., On the classification of Lorentzian Sasaki space forms, Publications de l’Institut Mathématique Nouvelle série 94 (2013), no.108, 163-168.
• [7] Cappelletti Montano, B. and Di Terlizzi L., D-homothetic transformations for a generalization of contact metric manifolds, Bull. Belg.Math. Soc. 14 (2007), 277–289.
• [8] Di Terlizzi, L. and Pastore, A.M., K-manifolds locally described by Sasaki manifolds, An. St. Univ. Ovidius Constanta 21 (2013), no.3, 269–287.
• [9] Di Terlizzi, L. and Konderak, J.J., Examples of a generalization of contact metric structures on fibre bundles, J. of Geometry 87 (2007), 31–49.
• [10] Duggal, Krishan L. and Bejancu, Aurel, Lightlike submanifolds of semi-Riemannian manifolds and applications. Kluwer Acad. Publ., Dordrecht, 1996.
• [11] Goldberg, S.I. and Yano, K., On normal globally framed f -manifolds, Tôhoku Math. J., 22 (1970), 362–370.
• [12] Goldberg, S.I., On the existence of manifolds with an f -structure, Tensor, N. S. 26 (1972), 323-329.
• [13] Guediri, M. and Lafontaine, J., Sur la complétude des varietés pseudoriemanniennes, J. Geom. Phys. 15 (1995), 150–158.
• [14] Kobayashi,S. and Nomizu,K., Foundations of Differential Geometry, Vol. I, II Interscience Publish., New York, 1963,1969.
• [15] Kobayashi, M., and Tsuhiya, S., Invariant submanifolds of an f -manifold with complemented frames, Kodai Math. Semin. Rep. 24 (1972), 430–450.
• [16] O’Neill, B., Semi-Riemannian geometry. Academic Press, New York, 1983.
• [17] Takahashi, T., Sasakian manifold with pseudo-Riemannian metric, Tôhoku Math. J. 21 (1969), no.2, 271–290.
• [18] Tanno, S., The topology of contact Riemannian manifolds, Illinois J. Math. 12 (1968), 700–717.
• [19] Tanno, S., Sasakian manifolds with constant ϕ-holomorphic sectional curvature, Tôhoku Math. J. 21 (1969), no.3, 501–507.
• [20] Yano, K., On a structure defined by a tensor field of type (1, 1) satisfying f 3 + f = 0, Tensor (N.S.) 14 (1963), 99–109.
• [21] Wu, H., On the de Rham decomposition theorem, Illinois J. Math. 8 (1964), 291–311.