Tokyo Journal of Mathematics

Conformal Slant Riemannian Maps to Kähler Manifolds

Mehmet Akif AKYOL and Bayram ŞAHIN

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Abstract

As a generalization of slant submanifolds and slant Riemannian maps, we introduce conformal slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds. We give non-trivial examples, investigate the geometry of foliations and obtain decomposition theorems by using the existence of conformal Riemannian maps. Moreover, we also investigate the harmonicity of such maps and find necessary and sufficient conditions for conformal slant Riemannian maps to be totally geodesic.

Article information

Source
Tokyo J. Math., Volume 42, Number 1 (2019), 225-237.

Dates
First available in Project Euclid: 18 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1563436920

Mathematical Reviews number (MathSciNet)
MR3982056

Zentralblatt MATH identifier
07062216

Subjects
Primary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

Citation

AKYOL, Mehmet Akif; ŞAHIN, Bayram. Conformal Slant Riemannian Maps to Kähler Manifolds. Tokyo J. Math. 42 (2019), no. 1, 225--237. https://projecteuclid.org/euclid.tjm/1563436920


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References

  • M. A. Akyol and B. \dSahin, Conformal anti-invariant Riemannian maps to Kähler manifolds, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., to appear.
  • M. A. Akyol and B. \dSahin, Conformal anti-invariant submersions from almost Hermitian manifolds, Turkish J. Math. 40(1) (2016), 43–70.
  • P. Baird and J. C. Wood, Harmonic morphisms between Riemannian manifolds, Oxford, Clarendon Press, 2003.
  • J. L. Cabrerizo, A. Carriazo, L. M. Fernandez and M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42(1) (2000), 125–138.
  • B. Y. Chen, Geometry of slant submanifolds, Leuven, Katholieke Universiteit Leuven, 1990.
  • B. Y. Chen, Slant immersions, Bull. Austral. Math. Soc. 41(1) (1990), 135–147.
  • A. E. Fischer, Riemannian maps between Riemannian manifolds, Contemporary Math. 132 (1992), 331–366.
  • E. Garcia-Rio and D. N. Kupeli, Semi-Riemannian maps and their applications, Dortrecht, Kluwer Academic, 1999.
  • A. J. Jaiswal and A. Pandey, Non-existence of harmonic maps on trans-Sasakian manifolds, Lobachevskii J. Math. 37(2) (2016), 185–192.
  • T. Nore, Second fundamental form of a map, Ann. Mat. Pur. and Appl. 146 (1987), 281–310.
  • B. Panday, A. J. Jaiswal and R. H. Ojha, Necessary and sufficient conditions for the Riemannian map to be a harmonic map on cosymplectic manifolds, Proc. Nat. Acad. Sci. India Sect. A 85(2) (2015), 265–268.
  • K. S. Park and B. \dSahin, Semi-slant Riemannian maps into almost Hermitian manifolds, Czechoslovak Math. J. 64 (2014), 1045–1061.
  • K. S. Park, Almost h-semi-slant Riemannian maps to almost quaternionic Hermitian manifolds, Commun. Contemp. Math. 17(6) (2015), 23 pp.
  • R. Prasad and S. Pandey, Slant Riemannian maps from Kenmotsu manifolds into Riemannian manifolds, Global J. of Pure and Applied Mathematics 13(4) (2017), 1143–1155.
  • R. Prasad and S. Pandey, Slant Riemannian maps from an almost contact manifold, Filomat 31(13) (2017), 3999–4007.
  • B. \dSahin, Riemannian submersions, Riemannian maps in Hermitian geometry and their applications, London, Elsevier, Academic Press, 2017.
  • B. \dSahin, Slant Riemannian maps to Kähler manifolds, Int. J. Geom. Methods Mod. Phys. 10(2) (2013), 1250080, 12 pp.
  • B. \dSahin, Invariant and anti-invariant Riemannian maps to Kähler manifolds, Int. J. Geom. Methods Mod. Phys. 7(3) (2010), 337–355.
  • B. \dSahin, Conformal Riemannian maps between Riemannian manifolds, their harmonicity and decomposition theorems, Acta Appl. Math. 109 (2010), 829–847.
  • K. Yano and M. Kon, Structures on manifolds, Singapore, World Scientific, 1984.