Semi-slant submanifolds in a locally conformal Kaehler space form

Yıl 2023, Cilt: 52 Sayı: 5, 1206 - 1218, 31.10.2023

Vittoria Bonanzınga , Koji Matsumoto

https://doi.org/10.15672/hujms.1032768

Öz

In this paper, we consider semi-slant submanifolds in a locally conformal Kaehler manifold and a locally conformal Kaehler space form. We give inequalities for the length of the second fundamental form and the mean curvature and, using Gauss and Codazzi equations, we get many useful results in locally conformal Kaehler space form.

Anahtar Kelimeler

locally conformal Kaehler manifold, locally conformal Kaehler space form, semi-slant submanifold, mean curvature

Destekleyen Kurum

INdAM, Istituzionale di Alta Matematica

Teşekkür

This work was supported by the National Group for Algebraic and Geometric Structures, and their Applications (GNSAGA-INdAM), ITALY. The authors thank the National Group.

Kaynakça

• [1] P. Alegre, Slant submanifolds of Lorentzian Sasakian and Para Sasakian manifold, Taiwan. J. Math. 17 (3), 897 - 910, 2013.
• [2] A. Bejancu, $CR$-submanifolds of a Kaehler manifold I, Proc. Amer. Math. Soc. 69, 134 -142, 1978.
• [3] A. Bejancu, $CR$-submanifolds of a Kaehler manifold II, Trans. Amer. Math. Soc. 250, 333-345, 1979.
• [4] A. Bejancu, Geomerty of $CR$-submanifolds, D. Reidel Publishing Company, 1986.
• [5] J.L. Cabrerizo, A. Carriazo, L. M. Fernández, M. Fernández, Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (1), 125 -138, 2000.
• [6] J.L. Cabrerizo, A. Carriazo, L. M. Fernández, M. Fernández, Semi-slant submanifolds of a Sasakian manifold, Geom. Dedicata 78, 183-199, 1999.
• [7] B.Y. Chen, $CR$-submanifolds of a Kaehler manifold I, J. of Differ. Geom. 16, 305-322, 1981.
• [8] B.Y. Chen, $CR$-submanifolds of a Kaehler manifold II , J. of Differ. Geom. 16, 493- 509, 1981.
• [9] B.Y. Chen, Geometry of submanifolds, Marcel Dekker, New York, 1973.
• [10] B.Y. Chen, Geometry of slant submanifolds, Katholieke Univ. Leuven, 1990.
• [11] B.Y. Chen, Slant immersions, B. Aust. Math. Soc. 41, 135-147, 1990.
• [12] S. Dragomir, L. Ornea, Locally conformal Kähler geometry, Prog. Math. 155, Birkhäuser Boston, Inc., Boston, MA, 1998.
• [13] T. Kashiwada, Some properties of locally conformal Kähler manifolds, Hokkaido Math. J. 8, 191-198, 1979.
• [14] V.A. Khan, M. A. Khan, Semi-slant submanifolds of a nearly Kaehler manifold, Turk. J. Math. 31, 341-353, 2007.
• [15] K. Matsumoto, On $CR$-submanifolds of locally conformal Kähler manifolds I, J. Korean Math. Soc. 21, 49-61, 1984.
• [16] K. Matsumoto, On $CR$-submanifolds of locally conformal Kähler manifolds II, Tensor N. S. 45, 144-150, 1987.
• [17] N. Papaghiuc, Semi-slant submanifolds of a Kaehlerian manifold, An. St. Univ. Al. I. Cuza, Iasi, 40, 55-61, 1994.
• [18] B. Sahin, Slant submanifolds of an almost product Riemannian manifold, J. Korean Math. Soc. 43, 717-732, 2006.
• [19] B. Sahin, Warped product submanifolds of Kaehler manifolds with a slant factor, Ann. Pol. Math. 95, 207-226, 2009.
• [20] H.M. Tastan, S. Gerdan, Hemi-slant submanifolds of a locally conformal Kähler manifold, Int. Electron. J. Geom. 8 (2), 46-56, 2015.
• [21] H.M. Tastan, M. M. Tripathi, Semi-slant submanifolds of a locally conformal Kähler manifold, Ann. St. Al. I. Cuza Univ. Iasi, (N.S.), 62 (2), 337-347, 2016.
• [22] H.M. Tastan, S. Gerdan Aydin, Hemi-slant and Semi-slant submanifolds of Locally Conformal Kähler Manifolds, in: B.Y. Chen, M.H. Shahid, F. Al Solamy (eds) Complex Geometry of Slant Submanifolds, Springer, Singapore, 2022.
• [23] I. Vaisman, Locally conformal almost Kähler manifolds, Isr. J. Math. 24, 338-351, 1976.