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FRAMED-COMPLEX SUBMERSIONS

Year 2014, Volume: 2 Issue: 2, 9 - 21, 01.12.2014

Abstract

In this paper, we introduce the concept of framed-complex submersion from a framed metric manifold onto an almost Hermitian manifold.We investigate the influence of a given structure defined on the total manifold on the determination of the corresponding structure on the base manifold. Moreover, we provide an example, investigate various properties of theO’Neill’s tensors for such submersions, find the integrability of the horizontaldistribution. We also obtain curvature relations between the base manifoldand the total manifold

References

  • D.E. Blair, Geometry of manifolds with structural group U (n) × O(s), J. Differential Geom. 4(2)(1970), 155-167.
  • D. Chinea, Almost contact metric submersions, Rend. Circ. Mat. Palermo, II Ser. 34 (1985), 89-104. [3] K.L. Duggal, S. Ianus, A.M. Pastore, Maps interchanging f-structures and their harmonicity, Acta Applicandae Mathematicae 67 (2001), 91-115.
  • M. Falcitelli, S. Ianus, A.M. Pastore, Riemannian submersions and related topics, World Scientific, 2004.
  • S.I. Goldberg, K. Yano, On normal globally framed f −manifolds, Tˆohoku Math. Journal 22 (1970), 362-370.
  • S.I. Goldberg, K. Yano, Globally framed f −manifolds, Illinois Math. Journal 22 (1971), 456- 474.
  • Y. G¨und¨uzalp, B. S.ahin, Paracontact semi-Riemannian submersions, Turkish J.Math. 37(1) (2013), 114-128.
  • Y. G¨und¨uzalp, B. S.ahin, Para-contact para-complex semi-Riemannian submersions, Bull. Malays. Math. Sci. Soc. 37(1)(2014), 139-152.
  • Y. G¨und¨uzalp, Slant submersions from almost product Riemannian manifolds, Turkish J.Math. 37(5) (2013), 863-873.
  • Y. G¨und¨uzalp, Anti-Invariant Semi-Riemannian Submersions from Almost Para-Hermitian Manifolds, Journal of Function Spaces and Applications, ID 720623, 2013.
  • A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715-737.
  • S. Ianus, R. Mazzocco, G.E. Vilcu, Riemannian submersions from quaternionic manifolds, Acta Appl. Math. 104 (2008), 83-89.
  • S. Ianus,S. Marchiafava,G.E. Vilcu,Para-quaternionic CR-submanifolds of para- quaternionic K¨ahler Manifols and semi-Riemannian submersions, Central European Journal of Mathematics 8, 4 (2010),735-753.
  • S. Ianus, A.M. Ionescu, R. Mocanu, G.E. Vilcu, Riemannian submersions from almost contact metric Manifols, Abh. Math. Semin. Univ. Hamburg 81 (2011), 101-114.
  • B. O’Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459- 469.
  • L.D. Terlizzi, On invariant submanifolds of C-and S-manifolds, Acta Math. Hungar. 85(1999), 229-239. [17] J. Vanzura, Almost s-contact structures, Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat. 26(1972), 97-115. [18] G.E. Vilcu, 3-submersions from QR-hypersurfaces of quaternionic K¨ahler manifolds, Ann. Polon. Math. 98 (2010), 301-309.
  • B. Watson, Almost Hermitian submersions, J. Differential Geom. 11(1976), 147-165.
  • K. Yano, M. Kon, Structures on manifolds, World Scientific, 1984.
  • K. Yano, On a structure defined by a tensor field f satisfying f3+ f = 0, Tensor 14 (1963), 99-109. Department of Mathematics, Dicle University, 21280, Diyarbakır-Turkey
  • E-mail address: ygunduzalp@dicle.edu.tr
Year 2014, Volume: 2 Issue: 2, 9 - 21, 01.12.2014

Abstract

References

  • D.E. Blair, Geometry of manifolds with structural group U (n) × O(s), J. Differential Geom. 4(2)(1970), 155-167.
  • D. Chinea, Almost contact metric submersions, Rend. Circ. Mat. Palermo, II Ser. 34 (1985), 89-104. [3] K.L. Duggal, S. Ianus, A.M. Pastore, Maps interchanging f-structures and their harmonicity, Acta Applicandae Mathematicae 67 (2001), 91-115.
  • M. Falcitelli, S. Ianus, A.M. Pastore, Riemannian submersions and related topics, World Scientific, 2004.
  • S.I. Goldberg, K. Yano, On normal globally framed f −manifolds, Tˆohoku Math. Journal 22 (1970), 362-370.
  • S.I. Goldberg, K. Yano, Globally framed f −manifolds, Illinois Math. Journal 22 (1971), 456- 474.
  • Y. G¨und¨uzalp, B. S.ahin, Paracontact semi-Riemannian submersions, Turkish J.Math. 37(1) (2013), 114-128.
  • Y. G¨und¨uzalp, B. S.ahin, Para-contact para-complex semi-Riemannian submersions, Bull. Malays. Math. Sci. Soc. 37(1)(2014), 139-152.
  • Y. G¨und¨uzalp, Slant submersions from almost product Riemannian manifolds, Turkish J.Math. 37(5) (2013), 863-873.
  • Y. G¨und¨uzalp, Anti-Invariant Semi-Riemannian Submersions from Almost Para-Hermitian Manifolds, Journal of Function Spaces and Applications, ID 720623, 2013.
  • A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715-737.
  • S. Ianus, R. Mazzocco, G.E. Vilcu, Riemannian submersions from quaternionic manifolds, Acta Appl. Math. 104 (2008), 83-89.
  • S. Ianus,S. Marchiafava,G.E. Vilcu,Para-quaternionic CR-submanifolds of para- quaternionic K¨ahler Manifols and semi-Riemannian submersions, Central European Journal of Mathematics 8, 4 (2010),735-753.
  • S. Ianus, A.M. Ionescu, R. Mocanu, G.E. Vilcu, Riemannian submersions from almost contact metric Manifols, Abh. Math. Semin. Univ. Hamburg 81 (2011), 101-114.
  • B. O’Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459- 469.
  • L.D. Terlizzi, On invariant submanifolds of C-and S-manifolds, Acta Math. Hungar. 85(1999), 229-239. [17] J. Vanzura, Almost s-contact structures, Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat. 26(1972), 97-115. [18] G.E. Vilcu, 3-submersions from QR-hypersurfaces of quaternionic K¨ahler manifolds, Ann. Polon. Math. 98 (2010), 301-309.
  • B. Watson, Almost Hermitian submersions, J. Differential Geom. 11(1976), 147-165.
  • K. Yano, M. Kon, Structures on manifolds, World Scientific, 1984.
  • K. Yano, On a structure defined by a tensor field f satisfying f3+ f = 0, Tensor 14 (1963), 99-109. Department of Mathematics, Dicle University, 21280, Diyarbakır-Turkey
  • E-mail address: ygunduzalp@dicle.edu.tr
There are 19 citations in total.

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Journal Section Articles
Authors

YILMAZ Gündüzalp This is me

Publication Date December 1, 2014
Submission Date April 4, 2015
Published in Issue Year 2014 Volume: 2 Issue: 2

Cite

APA Gündüzalp, Y. (2014). FRAMED-COMPLEX SUBMERSIONS. Konuralp Journal of Mathematics, 2(2), 9-21.
AMA Gündüzalp Y. FRAMED-COMPLEX SUBMERSIONS. Konuralp J. Math. October 2014;2(2):9-21.
Chicago Gündüzalp, YILMAZ. “FRAMED-COMPLEX SUBMERSIONS”. Konuralp Journal of Mathematics 2, no. 2 (October 2014): 9-21.
EndNote Gündüzalp Y (October 1, 2014) FRAMED-COMPLEX SUBMERSIONS. Konuralp Journal of Mathematics 2 2 9–21.
IEEE Y. Gündüzalp, “FRAMED-COMPLEX SUBMERSIONS”, Konuralp J. Math., vol. 2, no. 2, pp. 9–21, 2014.
ISNAD Gündüzalp, YILMAZ. “FRAMED-COMPLEX SUBMERSIONS”. Konuralp Journal of Mathematics 2/2 (October 2014), 9-21.
JAMA Gündüzalp Y. FRAMED-COMPLEX SUBMERSIONS. Konuralp J. Math. 2014;2:9–21.
MLA Gündüzalp, YILMAZ. “FRAMED-COMPLEX SUBMERSIONS”. Konuralp Journal of Mathematics, vol. 2, no. 2, 2014, pp. 9-21.
Vancouver Gündüzalp Y. FRAMED-COMPLEX SUBMERSIONS. Konuralp J. Math. 2014;2(2):9-21.
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