An integral formula for bi-slant submanifolds in complex space forms

Temel Bulgular & Veri:We obtain an integral formula of Simons' type for bi-slant submanifolds of a complex space form with positive constant holomorphic sectional curvature.

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Sonuç & Katkı:We also discuss the same result in different submanifolds such as hemi-slant and semi-slant submanifolds.

🔬Tür:Araştırma Makalesi

📍Kapsam:Genişletilmiş Akademik Örneklem

⚙️Değişkenler:bi-slant submanifolds · minimal submanifolds · totally geodesic submanifolds

Abstract

The present paper deals with bi-slant submanifolds in complex space forms. We obtain an integral formula of Simons' type for bi-slant submanifolds of a complex space form with positive constant holomorphic sectional curvature. Then, we apply it to prove our main result. We also discuss the same result in different submanifolds such as hemi-slant and semi-slant submanifolds.

Anahtar kelimeler

bi-slant submanifolds minimal submanifolds totally geodesic submanifolds complex space forms

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Bu Makaleye Atıf Yap

Özgür, C., Siddiqui, A. N. (2022). An integral formula for bi-slant submanifolds in complex space forms. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 6, 2028–2036. https://ajindex.com/articles/530050

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Kaynakça (21)

K. Abe, Applications of Riccati type differential equation to Riemannian manifolds with totally geodesic distributions, Tohoku Math. J. 25 (2), 425–444, 1973
A. Bejancu, Geometry of CR-submanifolds, Mathematics and its Applications, (East European Series), 23. D. Reidel Publishing Co., Dordrecht, 1986
A. Bejancu, M. Kon and K. Yano, CR-submanifolds of a complex space form, J. Differential Geom. 16 (1) 137–145, 1981
J.L. Cabrerizo, A. Carriazo, L.M. Fernández and M. Fernández, Semi-slant submanifolds of a Sasakian manifold, Geom. Dedicata 78 (2), 183–199, 1999
J.L. Cabrerizo, A. Carriazo, L.M. Fernández and M. Fernández, Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (1), 125–138, 2000
J.L. Cabrerizo, A. Carriazo, L.M. Fernández and M. Fernández, Structure on slant submanifold of a contact manifold, Indian J. Pure Appl. Math. 31 (7), 857–864, 2000
A. Carriazo, Bi-slant immersions, in: Proc. ICRAMS, 88–97, Kharagpur, India, 2000
B.-Y. Chen, Geometry of Submanifolds, Pure and Applied Mathematics, No
Marcel Dekker, Inc., New York, 1973
B.-Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit Leuven, Louvain, 1990
B.-Y. Chen, Slant immersions, Bull. Aust. Math. Soc. 41 (1), 135–147, 1990
B.-Y. Chen and D.E. Blair, On CR submanifolds of Hermitian manifolds, Israel J. Math. 34 (4), 353–363, 1979
B.-Y. Chen and S. Uddin, Warped product pointwise bi-slant submanifolds of Kaehler manifolds, Publ. Math. Debrecen 92, (1-2), 183–199, 2018
M. Gülbahar, E. Kılıç, and S. Keleş, A useful orthonormal basis on bi-slant submanifolds of almost Hermitian manifolds, Tamkang J. Math. 47 (2), 143–161, 2016
T. Ikawa, On submanifolds in a space with Sasakian 3-structure, Colloq. Math. 47 (1), 47–57, 1982
T. Ikawa, On some C-totally real submanifolds in a space with Sasakian 3-structure, Colloq. Math. 49 (1), 27–32, 1984
A. Mihai and I. Mihai, CR-submanifolds in complex and Sasakian space forms, in: Geometry of Cauchy-Riemann Submanifolds, 217–266, Springer, Singapore, 2016
N. Papaghiuc, Semi-slant submanifolds of a Kaehlerian manifold, An. Ştiinţ Al. I. Cuza Iaşi. Mat. 40 (1), 55–61, 1994
A.N. Siddiqui, M.H. Shahid and M. Jamali, Simons’ type formula for Kaehlerian slant submanifolds in complex space forms, Kyungpook Math. J. 58 (1), 149–165, 2018
J. Simons, Minimal varieties in Riemannian manifolds, Ann. Math. 88 (2), 62–105, 1968
B. Şahin, War