Research Article
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Year 2016, Volume: 9 Issue: 1, 1 - 8, 30.04.2016
https://doi.org/10.36890/iejg.591878

Abstract

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.

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

Year 2016, Volume: 9 Issue: 1, 1 - 8, 30.04.2016
https://doi.org/10.36890/iejg.591878

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.

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.
There are 21 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Letizia Brunetti This is me

Anna Maria Pastore This is me

Publication Date April 30, 2016
Published in Issue Year 2016 Volume: 9 Issue: 1

Cite

APA Brunetti, L., & Pastore, A. M. (2016). S-Manifolds Versus Indefinite S-Manifolds and Local Decomposition Theorems. International Electronic Journal of Geometry, 9(1), 1-8. https://doi.org/10.36890/iejg.591878
AMA Brunetti L, Pastore AM. S-Manifolds Versus Indefinite S-Manifolds and Local Decomposition Theorems. Int. Electron. J. Geom. April 2016;9(1):1-8. doi:10.36890/iejg.591878
Chicago Brunetti, Letizia, and Anna Maria Pastore. “S-Manifolds Versus Indefinite S-Manifolds and Local Decomposition Theorems”. International Electronic Journal of Geometry 9, no. 1 (April 2016): 1-8. https://doi.org/10.36890/iejg.591878.
EndNote Brunetti L, Pastore AM (April 1, 2016) S-Manifolds Versus Indefinite S-Manifolds and Local Decomposition Theorems. International Electronic Journal of Geometry 9 1 1–8.
IEEE L. Brunetti and A. M. Pastore, “S-Manifolds Versus Indefinite S-Manifolds and Local Decomposition Theorems”, Int. Electron. J. Geom., vol. 9, no. 1, pp. 1–8, 2016, doi: 10.36890/iejg.591878.
ISNAD Brunetti, Letizia - Pastore, Anna Maria. “S-Manifolds Versus Indefinite S-Manifolds and Local Decomposition Theorems”. International Electronic Journal of Geometry 9/1 (April 2016), 1-8. https://doi.org/10.36890/iejg.591878.
JAMA Brunetti L, Pastore AM. S-Manifolds Versus Indefinite S-Manifolds and Local Decomposition Theorems. Int. Electron. J. Geom. 2016;9:1–8.
MLA Brunetti, Letizia and Anna Maria Pastore. “S-Manifolds Versus Indefinite S-Manifolds and Local Decomposition Theorems”. International Electronic Journal of Geometry, vol. 9, no. 1, 2016, pp. 1-8, doi:10.36890/iejg.591878.
Vancouver Brunetti L, Pastore AM. S-Manifolds Versus Indefinite S-Manifolds and Local Decomposition Theorems. Int. Electron. J. Geom. 2016;9(1):1-8.