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 \(-s\).

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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).

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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

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Section

Research Article