Research Article
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Year 2011, Volume: 4 Issue: 2, 168 - 183, 30.10.2011

Anna Maria Pastore Vincenzo Saltarelli

Abstract

References

  • [1] Blair, D. E., Riemannian geometry of contact and symplectic manifolds, Progr. Math., 203, Birkhäuser Boston, Boston, MA, 2002.
  • [2] Blair, D. E., Koufogiorgos, T. and Papantoniou, B. J., Contact metric manifolds satisfying a nullity condition, Israel J. Math. 91 (1995), 189–214.
  • [3] Boeckx, E., A full classification of contact (k, µ)–spaces, Illinois J. Math. 44 (2000), 212–219.
  • [4] Dacko, P., On almost cosymplectic manifolds with the structure vector field ξ belonging tothe k-nullity distribution, BJGA, 5 No.2 (2000) 47–60.
  • [5] Dacko, P. and Olszak, Z., On almost cosymplectic (k, µ, ν)-spaces, in: PDEs, Submanifolds and Affine Differential Geometry, Banach Center Publications, Vol 69, pp. 211–220, Institute of Mathematics, Polish Academy of Sciences, Warszawa, 2005.
  • [6] Dacko, P. and Olszak, Z., On almost cosymplectic (−1, µ, 0)-space, Centr. Eur. J. Math. 3 No. 2 (2005), 318–330.
  • [7] Dileo, G. and Pastore, A. M., Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin 14 (2007), 343–354.
  • [8] Dileo, G. and Pastore, A. M., Almost Kenmotsu manifolds and nullity distributions, J. Geom. 93 (2009), 46–61.
  • [9] Dileo, G. and Pastore, A. M., Almost Kenmotsu manifolds with a condition of η-parallelism, Differential Geom. Appl. 27 (2009), 671–679.
  • [10] Falcitelli, M. and Pastore, A. M., Almost Kenmotsu f -manifolds, Balkan J. Geom. Appl. 12 (2007), no. 1, 32–43.
  • [11] Gouli-Andreou, F. and Xenos, P. J., A class of contact metric 3–manifolds with ξ ∈ N (k, µ) and k, µ functions, Algebras Groups Geom. 17 (2000), 401–407.
  • [12] Gray, A., Spaces of constancy of curvature operators, Proc. Amer. Math. Soc. 17 (1966), 897–902.
  • [13] Janssens, D. and Vanhecke, L., Almost contact structures and curvatures tensors, Kodai Math. J. 4 (1981), no. 1, 1–27.
  • [14] Kenmotsu, K., A class of almost contact Riemannian manifolds, Tˆohoku Math. J. 24 (1972), 93–103.
  • [15] Kim, T. W. and Pak, H. K., Canonical foliations of certain classes of almost contact metric structures, Acta Math. Sin. (Engl. Ser.) 21 (2005), no. 4, 841–846.
  • [16] Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, Vol. I, II, Interscience Publishers, New York, 1963, 1969.
  • [17] Koufogiorgos, T. and Tsichlias, C., On the existence of a new class of contact metric mani- folds, Canad. Math. Bull. Vol. 43 (2000), no. 4, 440–447.
  • [18] Olszak, Z., Locally conformal almost cosymplectic manifolds, Colloq. Math. 57 (1989), 73–87.
  • [19] Pastore, A. M. and Saltarelli, V., Almost Kenmotsu manifolds with conformal Reeb foliation, Bull. Belg. Math. Soc. Simon Stevin 18 (2011) (to appear).
  • [20] Tanno, S., Some differential equations on Riemannian manifolds, J. Math. Soc. Japan, 30 (1978), 509–531.

GENERALIZED NULLITY CONDITIONS ON ALMOST KENMOTSU MANIFOLDS

Year 2011, Volume: 4 Issue: 2, 168 - 183, 30.10.2011

Anna Maria Pastore Vincenzo Saltarelli

Abstract


Keywords

Almost Kenmotsu manifolds generalized nullity distributions

References

  • [1] Blair, D. E., Riemannian geometry of contact and symplectic manifolds, Progr. Math., 203, Birkhäuser Boston, Boston, MA, 2002.
  • [2] Blair, D. E., Koufogiorgos, T. and Papantoniou, B. J., Contact metric manifolds satisfying a nullity condition, Israel J. Math. 91 (1995), 189–214.
  • [3] Boeckx, E., A full classification of contact (k, µ)–spaces, Illinois J. Math. 44 (2000), 212–219.
  • [4] Dacko, P., On almost cosymplectic manifolds with the structure vector field ξ belonging tothe k-nullity distribution, BJGA, 5 No.2 (2000) 47–60.
  • [5] Dacko, P. and Olszak, Z., On almost cosymplectic (k, µ, ν)-spaces, in: PDEs, Submanifolds and Affine Differential Geometry, Banach Center Publications, Vol 69, pp. 211–220, Institute of Mathematics, Polish Academy of Sciences, Warszawa, 2005.
  • [6] Dacko, P. and Olszak, Z., On almost cosymplectic (−1, µ, 0)-space, Centr. Eur. J. Math. 3 No. 2 (2005), 318–330.
  • [7] Dileo, G. and Pastore, A. M., Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin 14 (2007), 343–354.
  • [8] Dileo, G. and Pastore, A. M., Almost Kenmotsu manifolds and nullity distributions, J. Geom. 93 (2009), 46–61.
  • [9] Dileo, G. and Pastore, A. M., Almost Kenmotsu manifolds with a condition of η-parallelism, Differential Geom. Appl. 27 (2009), 671–679.
  • [10] Falcitelli, M. and Pastore, A. M., Almost Kenmotsu f -manifolds, Balkan J. Geom. Appl. 12 (2007), no. 1, 32–43.
  • [11] Gouli-Andreou, F. and Xenos, P. J., A class of contact metric 3–manifolds with ξ ∈ N (k, µ) and k, µ functions, Algebras Groups Geom. 17 (2000), 401–407.
  • [12] Gray, A., Spaces of constancy of curvature operators, Proc. Amer. Math. Soc. 17 (1966), 897–902.
  • [13] Janssens, D. and Vanhecke, L., Almost contact structures and curvatures tensors, Kodai Math. J. 4 (1981), no. 1, 1–27.
  • [14] Kenmotsu, K., A class of almost contact Riemannian manifolds, Tˆohoku Math. J. 24 (1972), 93–103.
  • [15] Kim, T. W. and Pak, H. K., Canonical foliations of certain classes of almost contact metric structures, Acta Math. Sin. (Engl. Ser.) 21 (2005), no. 4, 841–846.
  • [16] Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, Vol. I, II, Interscience Publishers, New York, 1963, 1969.
  • [17] Koufogiorgos, T. and Tsichlias, C., On the existence of a new class of contact metric mani- folds, Canad. Math. Bull. Vol. 43 (2000), no. 4, 440–447.
  • [18] Olszak, Z., Locally conformal almost cosymplectic manifolds, Colloq. Math. 57 (1989), 73–87.
  • [19] Pastore, A. M. and Saltarelli, V., Almost Kenmotsu manifolds with conformal Reeb foliation, Bull. Belg. Math. Soc. Simon Stevin 18 (2011) (to appear).
  • [20] Tanno, S., Some differential equations on Riemannian manifolds, J. Math. Soc. Japan, 30 (1978), 509–531.
There are 20 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Anna Maria Pastore This is me

Vincenzo Saltarelli This is me

Publication Date October 30, 2011
Published in Issue Year 2011 Volume: 4 Issue: 2

Cite

APA Pastore, A. M., & Saltarelli, V. (2011). GENERALIZED NULLITY CONDITIONS ON ALMOST KENMOTSU MANIFOLDS. International Electronic Journal of Geometry, 4(2), 168-183.
AMA Pastore AM, Saltarelli V. GENERALIZED NULLITY CONDITIONS ON ALMOST KENMOTSU MANIFOLDS. Int. Electron. J. Geom. October 2011;4(2):168-183.
Chicago Pastore, Anna Maria, and Vincenzo Saltarelli. “GENERALIZED NULLITY CONDITIONS ON ALMOST KENMOTSU MANIFOLDS”. International Electronic Journal of Geometry 4, no. 2 (October 2011): 168-83.
EndNote Pastore AM, Saltarelli V (October 1, 2011) GENERALIZED NULLITY CONDITIONS ON ALMOST KENMOTSU MANIFOLDS. International Electronic Journal of Geometry 4 2 168–183.
IEEE A. M. Pastore and V. Saltarelli, “GENERALIZED NULLITY CONDITIONS ON ALMOST KENMOTSU MANIFOLDS”, Int. Electron. J. Geom., vol. 4, no. 2, pp. 168–183, 2011.
ISNAD Pastore, Anna Maria - Saltarelli, Vincenzo. “GENERALIZED NULLITY CONDITIONS ON ALMOST KENMOTSU MANIFOLDS”. International Electronic Journal of Geometry 4/2 (October 2011), 168-183.
JAMA Pastore AM, Saltarelli V. GENERALIZED NULLITY CONDITIONS ON ALMOST KENMOTSU MANIFOLDS. Int. Electron. J. Geom. 2011;4:168–183.
MLA Pastore, Anna Maria and Vincenzo Saltarelli. “GENERALIZED NULLITY CONDITIONS ON ALMOST KENMOTSU MANIFOLDS”. International Electronic Journal of Geometry, vol. 4, no. 2, 2011, pp. 168-83.
Vancouver Pastore AM, Saltarelli V. GENERALIZED NULLITY CONDITIONS ON ALMOST KENMOTSU MANIFOLDS. Int. Electron. J. Geom. 2011;4(2):168-83.