Abstract
References
- At¸ceken, M. Geometry of warped product semi-invariant submanifolds of a locally Riemann- ian product manifold, Serdica Math. J. 35 (3), 273–286, 2009.
- Bejancu, A. Semi-invariant submanifolds of locally product Riemannian manifold, Ann. Univ. Timisoara S. Math. XXII, 3–11, 1984.
- Bishop, R. L. and O’Neill, B. Manifolds of negative curvature, Trans Amer. Math. Soc. 145, 1–49, 1969.
- Chen, B. Geometry of warped product CR-submanifolds in Kaehler manifolds, Manotsh. Math. 133, 177–195, 2001.
- Matsumoto, K. On submanifolds of locally product Riemannian manifolds, TRU Math. 18(2), 145–157, 1982.
- Yano, K. and Kon, M. Structures on manifolds (World Scientific Publishing Co. Ltd, 1984).
- Tachibana, S. Some theorems on a locally product Riemannian manifold, Tohoku Math. J. 12, 281–292, 1960.
Abstract
Warped product semi-invariant submanifolds were defined and studied in locally Riemannian product manifolds in (K. Matsumoto, On submanifolds of locally product Riemannian manifolds, TRU Math. 18 (2), 145–157, 1982). In this paper, we go on to study warped product semi-invariant submanifolds in locally decomposable Riemannian manifolds. We prove several fundamental properties of warped product semi-invariant submanifolds, and establish a general inequality for a warped product semi-invariant submanifold in a locally decomposable
Riemannian manifold. After that, we investigate warped product semiinvariant submanifolds in a locally decomposable Riemannian manifold which satisfy the equality case of the inequality and obtain some new results.
Keywords
Semi-invariant submanifold Warped product semi-invariant submanifold Locally decomposable Riemannian manifold 2000 AMS Classification: Primary: 53C15; Secondary: 53C42
References
- At¸ceken, M. Geometry of warped product semi-invariant submanifolds of a locally Riemann- ian product manifold, Serdica Math. J. 35 (3), 273–286, 2009.
- Bejancu, A. Semi-invariant submanifolds of locally product Riemannian manifold, Ann. Univ. Timisoara S. Math. XXII, 3–11, 1984.
- Bishop, R. L. and O’Neill, B. Manifolds of negative curvature, Trans Amer. Math. Soc. 145, 1–49, 1969.
- Chen, B. Geometry of warped product CR-submanifolds in Kaehler manifolds, Manotsh. Math. 133, 177–195, 2001.
- Matsumoto, K. On submanifolds of locally product Riemannian manifolds, TRU Math. 18(2), 145–157, 1982.
- Yano, K. and Kon, M. Structures on manifolds (World Scientific Publishing Co. Ltd, 1984).
- Tachibana, S. Some theorems on a locally product Riemannian manifold, Tohoku Math. J. 12, 281–292, 1960.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Research Article |
| Authors | |
| Publication Date | March 1, 2011 |
| IZ | https://izlik.org/JA65LX59PN |
| Published in Issue | Year 2011 Volume: 40 Issue: 3 |