Research Article
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Year 2019, Volume: 12 Issue: 1, 32 - 42, 27.03.2019

Mohd Danish Siddiqi , Mehmet Akif Akyol

Abstract

References

  • [1] Akyol M. A., Conformal anti-invariant submersions from cosymplectic manifolds. Hacet. J. Math. Stat. 46(2) (2017), 177-192.
  • [2] Cengizhan M. and Erken I.K., Anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian submersions. Filomat 29(7) (2015), 1429-1444.
  • [3] Chinea, C., Almost contact metric submersions. Rend. Circ. Mat. Palermo 43(1) (1985), 89-104.
  • [4] Eells, J. and Sampson, J. H., Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86 (1964), 109-160.
  • [5] Falcitelli, M., Ianus, S. and Pastore, A. M., Riemannian submersions and Related topics, World Scientific, River Edge, NJ, 2004.
  • [6] Gündüzalp, Y., Anti-invariant semi-Riemannian submersions from almost para Hermitian manifolds. Journal of Function Spaces and Applications 2013, Art. ID 720623, 7 pp.
  • [7] Gray, A., Pseudo-Riemannian almost product manifolds and submersion. J. Math. Mech. 16 (1967), 715-737.
  • [8] Ianus, S. and Pastore, A. M., Harmonic maps on contact metric manifolds. Ann. Math. Blaise Pascal 2(2) (1995), 43-53.
  • [9] Lee, J. W., Anti-invariant ?􀀀 Riemannian submersions from almost contact manifolds. Hacettepe J. Math. Stat. 42(2)(2013), 231-241. [10] O’Neill, B., The fundamental equations of a submersions. Mich. Math. J. 13 (1996), 458-469.
  • [11] Park, K.S., H-anti-invariant submersions from almost quaternionic Hermitian manifolds. Czechoslovak Math. J. 67(2) (2017), 557-578.
  • [12] Siddiqi, M. D., Ahmed, M and Ojha, J.P., CR-submanifolds of nearly-trans hyperbolic sasakian manifolds admitting semi-symmetric non-metric connection. African J. Diaspora 17(10) (2014), 93-105.
  • [13] Siddiqi, M. D. and Akyol, M. A., Anti-invariant ξ^⊥-Riemannian Submersions from hyperbolic -Kenmotsu Manifolds. CUBO A Mathematical Journal 20(1) (2018), 79-94.
  • [14] Sahin, B., Anti-invariant Riemannian submersions from almost hermition manifolds. Cent. Eur. J. Math. 8(3) (2010), 437-447.
  • [15] Şahin B., Riemannian submersions from almost Hermitian manifolds. Taiwanese J. Math. 17 (2012), 629-659.
  • [16] Şahin B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications. San Diego, CA, USA: Academic Press, 2017.
  • [17] Taştan, H. M. and Gerdan, S., Clairaut Anti-invariant Submersions from Sasakian and Kenmotsu Manifolds. Mediterranean J. Math. 14 (2017), no. 6, Art. 235, 17 pp.
  • [18] Upadhyay, M. D. and Dube., K. K., Almost contact hyperbolic (f, g, η, ξ) structure. Acta. Math. Acad. Scient. Hung 28 (1976), 1-4.
  • [19] Watson, B. Almost Hermitian submersions. J. Differential Geometry 11(1) (1976), 147-165.

Anti-invariant ξ^⊥-Riemannian Submersions From Almost Hyperbolic Contact Manifolds

Year 2019, Volume: 12 Issue: 1, 32 - 42, 27.03.2019

Mohd Danish Siddiqi , Mehmet Akif Akyol

Abstract

In this paper, we introduce anti-invariant  ξ^⊥-Riemannian submersions from almost hyperbolic
contact manifolds onto Riemannian manifolds. Necessary and sufficient conditions for a special
anti-invariant  ξ^⊥-Riemannian submersion to be totally geodesic are studied. Moreover, we obtain
decomposition theorems for the total manifold of such submersions.

Keywords

Riemannian submersion Anti-invariant ξ^⊥-Riemannian submersions Trans Hyperbolic Sasakian manifold Integrability Conditions

References

  • [1] Akyol M. A., Conformal anti-invariant submersions from cosymplectic manifolds. Hacet. J. Math. Stat. 46(2) (2017), 177-192.
  • [2] Cengizhan M. and Erken I.K., Anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian submersions. Filomat 29(7) (2015), 1429-1444.
  • [3] Chinea, C., Almost contact metric submersions. Rend. Circ. Mat. Palermo 43(1) (1985), 89-104.
  • [4] Eells, J. and Sampson, J. H., Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86 (1964), 109-160.
  • [5] Falcitelli, M., Ianus, S. and Pastore, A. M., Riemannian submersions and Related topics, World Scientific, River Edge, NJ, 2004.
  • [6] Gündüzalp, Y., Anti-invariant semi-Riemannian submersions from almost para Hermitian manifolds. Journal of Function Spaces and Applications 2013, Art. ID 720623, 7 pp.
  • [7] Gray, A., Pseudo-Riemannian almost product manifolds and submersion. J. Math. Mech. 16 (1967), 715-737.
  • [8] Ianus, S. and Pastore, A. M., Harmonic maps on contact metric manifolds. Ann. Math. Blaise Pascal 2(2) (1995), 43-53.
  • [9] Lee, J. W., Anti-invariant ?􀀀 Riemannian submersions from almost contact manifolds. Hacettepe J. Math. Stat. 42(2)(2013), 231-241. [10] O’Neill, B., The fundamental equations of a submersions. Mich. Math. J. 13 (1996), 458-469.
  • [11] Park, K.S., H-anti-invariant submersions from almost quaternionic Hermitian manifolds. Czechoslovak Math. J. 67(2) (2017), 557-578.
  • [12] Siddiqi, M. D., Ahmed, M and Ojha, J.P., CR-submanifolds of nearly-trans hyperbolic sasakian manifolds admitting semi-symmetric non-metric connection. African J. Diaspora 17(10) (2014), 93-105.
  • [13] Siddiqi, M. D. and Akyol, M. A., Anti-invariant ξ^⊥-Riemannian Submersions from hyperbolic -Kenmotsu Manifolds. CUBO A Mathematical Journal 20(1) (2018), 79-94.
  • [14] Sahin, B., Anti-invariant Riemannian submersions from almost hermition manifolds. Cent. Eur. J. Math. 8(3) (2010), 437-447.
  • [15] Şahin B., Riemannian submersions from almost Hermitian manifolds. Taiwanese J. Math. 17 (2012), 629-659.
  • [16] Şahin B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications. San Diego, CA, USA: Academic Press, 2017.
  • [17] Taştan, H. M. and Gerdan, S., Clairaut Anti-invariant Submersions from Sasakian and Kenmotsu Manifolds. Mediterranean J. Math. 14 (2017), no. 6, Art. 235, 17 pp.
  • [18] Upadhyay, M. D. and Dube., K. K., Almost contact hyperbolic (f, g, η, ξ) structure. Acta. Math. Acad. Scient. Hung 28 (1976), 1-4.
  • [19] Watson, B. Almost Hermitian submersions. J. Differential Geometry 11(1) (1976), 147-165.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Mohd Danish Siddiqi

Mehmet Akif Akyol

Publication Date March 27, 2019
Published in Issue Year 2019 Volume: 12 Issue: 1

Cite

APA Siddiqi, M. D., & Akyol, M. A. (2019). Anti-invariant ξ^⊥-Riemannian Submersions From Almost Hyperbolic Contact Manifolds. International Electronic Journal of Geometry, 12(1), 32-42.
AMA Siddiqi MD, Akyol MA. Anti-invariant ξ^⊥-Riemannian Submersions From Almost Hyperbolic Contact Manifolds. Int. Electron. J. Geom. March 2019;12(1):32-42.
Chicago Siddiqi, Mohd Danish, and Mehmet Akif Akyol. “Anti-Invariant ξ^⊥-Riemannian Submersions From Almost Hyperbolic Contact Manifolds”. International Electronic Journal of Geometry 12, no. 1 (March 2019): 32-42.
EndNote Siddiqi MD, Akyol MA (March 1, 2019) Anti-invariant ξ^⊥-Riemannian Submersions From Almost Hyperbolic Contact Manifolds. International Electronic Journal of Geometry 12 1 32–42.
IEEE M. D. Siddiqi and M. A. Akyol, “Anti-invariant ξ^⊥-Riemannian Submersions From Almost Hyperbolic Contact Manifolds”, Int. Electron. J. Geom., vol. 12, no. 1, pp. 32–42, 2019.
ISNAD Siddiqi, Mohd Danish - Akyol, Mehmet Akif. “Anti-Invariant ξ^⊥-Riemannian Submersions From Almost Hyperbolic Contact Manifolds”. International Electronic Journal of Geometry 12/1 (March2019), 32-42.
JAMA Siddiqi MD, Akyol MA. Anti-invariant ξ^⊥-Riemannian Submersions From Almost Hyperbolic Contact Manifolds. Int. Electron. J. Geom. 2019;12:32–42.
MLA Siddiqi, Mohd Danish and Mehmet Akif Akyol. “Anti-Invariant ξ^⊥-Riemannian Submersions From Almost Hyperbolic Contact Manifolds”. International Electronic Journal of Geometry, vol. 12, no. 1, 2019, pp. 32-42.
Vancouver Siddiqi MD, Akyol MA. Anti-invariant ξ^⊥-Riemannian Submersions From Almost Hyperbolic Contact Manifolds. Int. Electron. J. Geom. 2019;12(1):32-4.
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