TAILIEUCHUNG - The geometry of hemi-slant submanifolds of a locally product Riemannian manifold

In the present paper, we study hemi-slant submanifolds of a locally product Riemannian manifold. We prove that the anti-invariant distribution involved in the definition of hemi-slant submanifold is integrable and give some applications of this result. | Turkish Journal of Mathematics Research Article Turk J Math (2015) 39 ¨ ITAK ˙ c TUB ⃝ doi: The geometry of hemi-slant submanifolds of a locally product Riemannian manifold ¨ ˙ 2 Hakan Mete TAS ¸ TAN1,∗, Fatma OZDEM IR ˙ ˙ Department of Mathematics, Istanbul University, Vezneciler, Istanbul, Turkey 2 ˙ ˙ Department of Mathematics, Istanbul Technical University, Maslak, Istanbul, Turkey 1 Received: • Accepted: • Published Online: • Printed: Abstract: In the present paper, we study hemi-slant submanifolds of a locally product Riemannian manifold. We prove that the anti-invariant distribution involved in the definition of hemi-slant submanifold is integrable and give some applications of this result. We get a necessary and sufficient condition for a proper hemi-slant submanifold to be a hemi-slant product. We also study these types of submanifolds with parallel canonical structures. Moreover, we give two characterization theorems for the totally umbilical proper hemi-slant submanifolds. Finally, we obtain a basic inequality involving Ricci curvature and the squared mean curvature of a hemi-slant submanifold of a certain type of locally product Riemannian manifolds. Key words: Locally product manifold, hemi-slant submanifold, slant distribution 1. Introduction Study of slant submanifolds was initiated by Chen [8], as a generalization of both holomorphic and totally real submanifolds of a K¨ahler manifold. Slant submanifolds have been studied in different kind of structures: almost contact [13], neutral K¨ahler [4], Lorentzian Sasakian [2], and Sasakian [6] by several geometers. N. Papaghiuc [14] introduced semi-slant submanifolds of a K¨ahler manifold as a natural generalization of slant submanifold. Carriazo [7], introduced bi-slant submanifolds of an almost Hermitian manifold as a generalization of semi-slant submanifolds. One of the classes of bi-slant .

• Toán học
• Locally product manifold
• Hemi slant submanifold
• Slant distribution
• Riemannian manifold
• Parallel canonical structures
• Almost product Riemannian manifold
• Special slant surface
• Pointwise slant submanifolds
• Mean curvature
• Gauss curvature
• Kaehlerian product manifold
• Mixed geodesic submanifold
• Locally decomposable Riemannian manifold
• Constant holomorphic sectional curved manifold
• Riemannian product manifold
• Warped product submanifold
• Skew semi invariant submanifold
• Invariant distribution
• Semi invariant submanifolds
• Riemannian product
• Warped product
• Locally Riemannian product manifold
• Degenerate metric
• Semi Riemannian
• Product manifold
• R lightlike submanifold
• Locally Riemannian product