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The Fischer-Marsden Solutions on Almost CoKähler Manifold

Year 2017, Volume: 10 Issue: 1, 15 - 20, 30.04.2017
https://doi.org/10.36890/iejg.584436

Abstract


References

  • [1] Besse, A., Einstein manifolds. Springer-Verlag, New York, 2008.
  • [2] Blair, D. E., Riemannian geometry of contact and symplectic manifolds. Birkhauser, Boston, 2002.
  • [3] Bourguignon, J. P., Une stratifcation de l’espace des structures riemanniennes. Compositio Math., 30 (1975), 1-41.
  • [4] Blair, D. E., Koufogiorgos, T. and Papantoniou, B. J., Contact metric manifolds satisfying a nullity condition. Israel J. of Math., 91 (1995), 189-214.
  • [5] Cernea, P. and Guan, D., Killing fields generated by multiple solutions to the Fischer-Marsden equation. International Journal of Math., 26(2015), 93-111.
  • [6] Corvino. J., Scalar curvature deformations and a gluing construction for the Einstein constraint equations. Commun. Math. Phys., 214(2000), 137-189.
  • [7] Fisher A. and Marsden. J., Manifolds of Riemannian metrics with prescribed scalar curvature. Bull. Am. Math. Soc., 80 (1974), 479-484.
  • [8] Kobayashi, O., A Differential Equation Arising From Scalar Curvature Function. J. Math. Soc. Japan, 34 (1982), 665-675.
  • [9] S. B. Myers: Connections between differential geometry and topology. Duke Math. J., 1 (1935), 376-391.
  • [10] Obata, O., Certain conditions for a Riemannian manifold to be isometric with a sphere. J. Math. Soc. Japan, 14 (1962), no. 3, 333-340.
  • [11] Olszak, Z., On contact metric manifolds. Tohoku Math. J., 31 (1979), 247-253.
  • [12] Shen, Y., A note on Fischer-Marsden’s conjecture. Proc. Am. Math. Soc., 125 (1997), 901-905.
  • [13] Tanno, S., The topology of contact Riemannian manifolds. Illinois J. Math., 12 (1968), 700-717.
  • [14] Patra, D. S. and Ghosh, A., Certain contact metrics satisfying Miao-Tam critical condition. Ann. Polon. Math., 116 (2016), no. 3, 263-271.
  • [15] Sharma, R., Certain results on K-contact and (k, µ)-contact manifolds. J. Geom., 89 (2008), no. (1-2), 138-147.
  • [16] Wang, Y., A Generalization of the Goldberg Conjecture for CoKa¨hler Manifolds. Mediterr. J. Math., 13 (2016), 2679-2690.
  • [17] Chinea, D., Le´on, M. de and Marrero, J. C., Topology of cosymplectic manifolds. J. Math. Pures Appl., 72 (1993), no. 6, 567-591.
  • [18] Marrero, J. C. and Padr´on, E., New examples of compact cosymplectic solvmanifolds. Arch. Math. (Brno), 34 (1998), no. 3, 337-345.
  • [19] Dacko, P. and Olszak, Z., On almost cosymplectic (k, µ, ν)-space. Banach Center Publ., 69 (2005), 211-220.
  • [20] Endo, H., Non-existence of almost cosymplectic manifolds satisfying a certain condition. Tensor (N. S.), 63 (2002), no. 3, 272-284.
  • [21] Gray, A., Spaces of contancy of curvature operators. Proc. Amer. Math. Soc. 17 (1966), 897-902.
  • [22] Patra, D. S. and Ghosh, A., Fischer-Marsden conjecture and contact geometry. comunicated.
Year 2017, Volume: 10 Issue: 1, 15 - 20, 30.04.2017
https://doi.org/10.36890/iejg.584436

Abstract

References

  • [1] Besse, A., Einstein manifolds. Springer-Verlag, New York, 2008.
  • [2] Blair, D. E., Riemannian geometry of contact and symplectic manifolds. Birkhauser, Boston, 2002.
  • [3] Bourguignon, J. P., Une stratifcation de l’espace des structures riemanniennes. Compositio Math., 30 (1975), 1-41.
  • [4] Blair, D. E., Koufogiorgos, T. and Papantoniou, B. J., Contact metric manifolds satisfying a nullity condition. Israel J. of Math., 91 (1995), 189-214.
  • [5] Cernea, P. and Guan, D., Killing fields generated by multiple solutions to the Fischer-Marsden equation. International Journal of Math., 26(2015), 93-111.
  • [6] Corvino. J., Scalar curvature deformations and a gluing construction for the Einstein constraint equations. Commun. Math. Phys., 214(2000), 137-189.
  • [7] Fisher A. and Marsden. J., Manifolds of Riemannian metrics with prescribed scalar curvature. Bull. Am. Math. Soc., 80 (1974), 479-484.
  • [8] Kobayashi, O., A Differential Equation Arising From Scalar Curvature Function. J. Math. Soc. Japan, 34 (1982), 665-675.
  • [9] S. B. Myers: Connections between differential geometry and topology. Duke Math. J., 1 (1935), 376-391.
  • [10] Obata, O., Certain conditions for a Riemannian manifold to be isometric with a sphere. J. Math. Soc. Japan, 14 (1962), no. 3, 333-340.
  • [11] Olszak, Z., On contact metric manifolds. Tohoku Math. J., 31 (1979), 247-253.
  • [12] Shen, Y., A note on Fischer-Marsden’s conjecture. Proc. Am. Math. Soc., 125 (1997), 901-905.
  • [13] Tanno, S., The topology of contact Riemannian manifolds. Illinois J. Math., 12 (1968), 700-717.
  • [14] Patra, D. S. and Ghosh, A., Certain contact metrics satisfying Miao-Tam critical condition. Ann. Polon. Math., 116 (2016), no. 3, 263-271.
  • [15] Sharma, R., Certain results on K-contact and (k, µ)-contact manifolds. J. Geom., 89 (2008), no. (1-2), 138-147.
  • [16] Wang, Y., A Generalization of the Goldberg Conjecture for CoKa¨hler Manifolds. Mediterr. J. Math., 13 (2016), 2679-2690.
  • [17] Chinea, D., Le´on, M. de and Marrero, J. C., Topology of cosymplectic manifolds. J. Math. Pures Appl., 72 (1993), no. 6, 567-591.
  • [18] Marrero, J. C. and Padr´on, E., New examples of compact cosymplectic solvmanifolds. Arch. Math. (Brno), 34 (1998), no. 3, 337-345.
  • [19] Dacko, P. and Olszak, Z., On almost cosymplectic (k, µ, ν)-space. Banach Center Publ., 69 (2005), 211-220.
  • [20] Endo, H., Non-existence of almost cosymplectic manifolds satisfying a certain condition. Tensor (N. S.), 63 (2002), no. 3, 272-284.
  • [21] Gray, A., Spaces of contancy of curvature operators. Proc. Amer. Math. Soc. 17 (1966), 897-902.
  • [22] Patra, D. S. and Ghosh, A., Fischer-Marsden conjecture and contact geometry. comunicated.
There are 22 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Dhriti Sundar Patra

Arindam Bhattacharyya

Manjusha Tarafdar This is me

Publication Date April 30, 2017
Published in Issue Year 2017 Volume: 10 Issue: 1

Cite

APA Patra, D. S., Bhattacharyya, A., & Tarafdar, M. (2017). The Fischer-Marsden Solutions on Almost CoKähler Manifold. International Electronic Journal of Geometry, 10(1), 15-20. https://doi.org/10.36890/iejg.584436
AMA Patra DS, Bhattacharyya A, Tarafdar M. The Fischer-Marsden Solutions on Almost CoKähler Manifold. Int. Electron. J. Geom. April 2017;10(1):15-20. doi:10.36890/iejg.584436
Chicago Patra, Dhriti Sundar, Arindam Bhattacharyya, and Manjusha Tarafdar. “The Fischer-Marsden Solutions on Almost CoKähler Manifold”. International Electronic Journal of Geometry 10, no. 1 (April 2017): 15-20. https://doi.org/10.36890/iejg.584436.
EndNote Patra DS, Bhattacharyya A, Tarafdar M (April 1, 2017) The Fischer-Marsden Solutions on Almost CoKähler Manifold. International Electronic Journal of Geometry 10 1 15–20.
IEEE D. S. Patra, A. Bhattacharyya, and M. Tarafdar, “The Fischer-Marsden Solutions on Almost CoKähler Manifold”, Int. Electron. J. Geom., vol. 10, no. 1, pp. 15–20, 2017, doi: 10.36890/iejg.584436.
ISNAD Patra, Dhriti Sundar et al. “The Fischer-Marsden Solutions on Almost CoKähler Manifold”. International Electronic Journal of Geometry 10/1 (April 2017), 15-20. https://doi.org/10.36890/iejg.584436.
JAMA Patra DS, Bhattacharyya A, Tarafdar M. The Fischer-Marsden Solutions on Almost CoKähler Manifold. Int. Electron. J. Geom. 2017;10:15–20.
MLA Patra, Dhriti Sundar et al. “The Fischer-Marsden Solutions on Almost CoKähler Manifold”. International Electronic Journal of Geometry, vol. 10, no. 1, 2017, pp. 15-20, doi:10.36890/iejg.584436.
Vancouver Patra DS, Bhattacharyya A, Tarafdar M. The Fischer-Marsden Solutions on Almost CoKähler Manifold. Int. Electron. J. Geom. 2017;10(1):15-20.