Abstract
In this paper, a \(3\)-Kenmotsu structure is defined on a \(4n+1\) dimensional manifold where such structure seems to be never studied before.
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REFERENCES
D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds (Birkhauser, Basel, 2002).
S. V. Galaev, ‘‘Admissible Hyper-Complex Pseudo-Hermitian Structures,’’ Lobachevskii J. Math. 39 (1), 71–76 (2018).
G. Ganchev and V. Mihova, ‘‘Warped product Kahler manifolds and Bochner–Kahler metrics,’’ J. Geom. Phys. 58, 803–824 (2008).
J. W. Gray, ‘‘Some global properties of contact structures,’’ Ann. Math. 69, 421–450 (1959).
S. Ishihara, ‘‘Quaternion Kählerian Manifolds,’’ J. Diff. Geom. 9, 483–500 (1974).
T. Kashiwada, ‘‘On a contact \(3\)-structure,’’ Math. Z. 238, 829–832 (2001).
K. Kenmotsu, ‘‘A class of almost contact Riemannian manifolds,’’ Tohoku Math. J. 24, 93–103 (1972).
Y. Y. Kuo, ‘‘On almost contact \(3\)-structure,’’ Tohoku Math. J. 22, 325–332 (1970).
J. M. Lee, Riemannian Manifolds, an Introduction to Curvature (Springer, New York, 1997).
P. Molino, Riemannian Foliations (Birkhauser, Univ. of Michigan, 1988).
Z. Olszak and R. Rosca, ‘‘Normally conformal almost symplectic manifolds,’’ Publ. Math. Debrecen 39, 315–323 (1991).
S. Sasaki, ‘‘On differentiable manifolds with certain structures which are closely related to almost contact structure I,’’ Tohoku Math. J. 12, 459–476 (1960).
S. Sasaki and Y. Hatakeyama, ‘‘On the differentiable manifolds with certain structures which are closely related to almost contact structure II,’’ Tohoku Math. J. 13, 281–294 (1961).
S. Sasaki and Y. Hatakeyama, ‘‘On differentiable manifolds with contact metric structures,’’ J. Math. Soc. Jpn. 14, 249–271 (1962).
S. I. Tachibana and W. N. Yu, ‘‘On a Riemannian space admitting more than one Sasakian structures,’’ Tohoku Math. J. 22, 536–540 (1970).
Y. Tashiro, ‘‘On contact structure of hypersurfaces in complex manifolds I,’’ Tohoku Math. J. 15 (2), 62–78 (1963).
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(Submitted by M. A.Malakhaltsev)
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Attarchi, H. \(\mathbf{3}\)-Kenmotsu Manifolds. Lobachevskii J Math 41, 320–325 (2020). https://doi.org/10.1134/S1995080220030051
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DOI: https://doi.org/10.1134/S1995080220030051