Generalized Kenmotsu Manifolds

Authors

  • Aysel Turgut Vanli Department of Mathematics, University of Gazi, Ankara
  • Ramazan Sari Merzifon Vocational Schools, Amasya University, Amasya

DOI:

https://doi.org/10.26713/cma.v7i4.471

Keywords:

Kenmotsu manifolds, metric f-manifolds, generalized Kenmotsu manifolds, semi-symmetric, Ricci semi-symmetric, projective semi-symmetric.

Abstract

In 1972, K. Kenmotsu studied a class of almost contact Riemannian manifolds which later are called a Kenmotsu manifold. In this paper, we study Kenmotsu manifolds with \((2n+s)\)-dimensional $s$-contact metric manifold that we call generalized Kenmotsu manifolds.\ Necessary and sufficient condition is given for a \(s\)-contact metric manifold to be a generalized Kenmotsu manifold. We show that a generalized Kenmotsu manifold is a locally warped product space. In addition, we study some curvature properties of generalized Kenmotsu manifolds. Moreover, we obtain that the \(\varphi\)-sectional curvature of any semi-symmetric and projective semi-symmetric \((2n+s)\)-dimensional generalized Kenmotsu manifold is \(-s\).

Downloads

Download data is not yet available.

References

L. Bhatt and K.K. Dube, Semi-invariant submanifolds of (r)-Kenmotsu manifolds, Acta Cienc, Indica Math. 29 (2003), 167–172.

T.Q. Binh, L. Tamassy, U.C. De and M. Taraftar, Same remarks on almost Kenmotsu manifolds, Math. Pan. 13 (2002), 31–39.

R.L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1–50.

D.E. Blair, Geometry of manifolds with structural group (U(n)times O(s)), J. Differ. Geom. 4 (1970), 155–167.

D.E. Blair, G. Ludden and K. Yano, Differential geometric structures on principal toroidal bundles, Trans. Amer. Mat. Soc. 181 (1973), 175–184.

D.E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, 2nd edition, Birkhauser, Boston (2010).

J.L. Cabrerizo, L.M. Fernandez and M. Fernandez, The curvature tensor fields on (f)-manifolds with complemented frames, An. Stiint. Univ. Cuza. Sect. Math. 36 (1990), 151–161.

U.C. De and G. Pathok, On 3-dimensional Kenmotsu manifolds, Indian J. Pure Appl. Math. 35 (2004), 159–165.

M. Falcitelli and A.M. Pastore, (f)-structures of Kenmotsu type, Mediterr. J. Math. 3 (2006), 549–564.

S.I. Goldberg, On the existence of manifolds with an (f)-structure, Tensor New. Ser. 26 (1972), 323–329.

S.I. Goldberg and K. Yano, Globally framed (f)-manifolds, III, J. Math., 15 (1971), 456–474.

S.I. Goldberg and K. Yano, On normal globally framed (f)-manifolds, Tohoku Math Journal 22 (1972), 362–370.

D. Janssens and L. Vanhecke, Almost contact structures and curvature tensors, Kodai Math. J. 4 (1981), 1–27.

J.B. Jun, U.C. De and G. Pathak, On Kenmotsu Manifolds, J. Korean Math. Soc. 42 (2005), 435–445.

K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24 (1972), 93–103.

H. Nakagawa, f -structures induced on submanifolds in spaces, almost Hermitian or Kaehlerian, Kodai Math. Sem. Rep. 18 (1966), 161–183.

H. Nakagawa, On framed f -manifolds, Kodai Math. Sem. Rep. 18 (1966), 293–306.

D.G. Prakasha, C.S. Bagewadi and N.S. Basavarajappa, On Lorentzian (beta)-Kenmotsu manifolds, Int. J. Math. Anal. 17 (2008), 919–927.

G. Pitis, Geometry of Kenmotsu Manifolds, Publishing House of Transilvania University of Brasov, Brasov (2007).

S. Tanno, The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J. 21 (1969), 21–38.

J. Vanzura, Almost (r)-contact structures, Ann. Scuola. Norm. Sup. Pisa. Sci. Fis. Mat. 26 (1972), 97–115.

K. Yano, On a structure defined by a tensor field f of type (1,1) satisfying (f^3 + f= 0), Tensor N.S. 14 (1963), 99–109.

K. Yano and M. Kon, Structure on Manifolds, World Scientific, Singapore (1984).

Downloads

Published

31-12-2016
CITATION

How to Cite

Vanli, A. T., & Sari, R. (2016). Generalized Kenmotsu Manifolds. Communications in Mathematics and Applications, 7(4), 311–328. https://doi.org/10.26713/cma.v7i4.471

Issue

Vol. 7 No. 4 (2016)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.