Results 11 to 20 of about 49 (49)
A note on Chen′s basic equality for submanifolds in a Sasakian space form
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 11, Page 711-716, 2003., 2003 It is proved that a Riemannian manifold M isometrically immersed in a Sasakian space form M˜(c) of constant φ‐sectional curvature c < 1, with the structure vector field ξ tangent to M, satisfies Chen′s basic equality if and only if it is a 3‐dimensional minimal invariant submanifold.
Mukut Mani Tripathi +2 more
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On the structure vector field of a real hypersurface in complex quadric
Open Mathematics, 2018 From the notion of Jacobi type vector fields for a real hypersurface in complex quadric Qm we prove that if the structure vector field is of Jacobi type it is Killing when the real hypersurface is either Hopf or compact.
Dios Pérez Juan de
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A basic inequality for submanifolds in a cosymplectic space form
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 9, Page 539-547, 2003., 2003 For submanifolds tangent to the structure vector field in cosymplectic space forms, we establish a basic inequality between the main intrinsic invariants of the submanifold, namely, its sectional curvature and scalar curvature on one side; and its main extrinsic invariant, namely, squared mean curvature on the other side.
Jeong-Sik Kim, Jaedong Choi
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Open Mathematics, 2018 In this paper, we obtain Chen’s inequalities for submanifolds in (κ, μ)-contact space form endowed with a semi-symmetric metric connection.
Ahmad Asif +3 more
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Constant mean curvature hypersurfaces with constant δ‐invariant
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 67, Page 4205-4216, 2003., 2003 We completely classify constant mean curvature hypersurfaces (CMC) with constant δ‐invariant in the unit 4‐sphere S4 and in the Euclidean 4‐space 𝔼4.
Bang-Yen Chen, Oscar J. Garay
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Ricci curvature of submanifolds in Kenmotsu space forms
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 12, Page 719-726, 2002., 2002 In 1999, Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Similar problems for submanifolds in complex space forms were studied by Matsumoto et al.
Kadri Arslan +4 more
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Global pinching theorems of submanifolds in spheres
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 3, Page 183-191, 2002., 2002 Let M be a compact embedded submanifold with parallel mean curvature vector and positive Ricci curvature in the unit sphere S n+p(n ≥ 2 , p ≥ 1). By using the Sobolev inequalities of P. Li (1980) to Lp estimate for the square length σ of the second fundamental form and the norm of a tensor Φ, related to the second fundamental form, we set up some ...
Kairen Cai
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On hypersurfaces in a locally affine Riemannian Banach manifold
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 6, Page 375-379, 2002., 2002 We prove that an essential hypersurface of second order in an infinite dimensional locally affine Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature.
El-Said R. Lashin, Tarek F. Mersal
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CR‐submanifolds of a nearly trans‐Sasakian manifold
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 3, Page 167-175, 2002., 2002 This paper considers the study of CR‐submanifolds of a nearly trans‐Sasakian manifold, generalizing the results of trans‐Sasakian manifolds and thus those of Sasakian manifolds.
Falleh R. Al-Solamy
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Submanifolds of F‐structure manifold satisfying FK + (−)K+1F = 0
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 3, Page 167-172, 2001., 2001 The purpose of this paper is to study invariant submanifolds of an n‐dimensional manifold M endowed with an F‐structure satisfying FK + (−)K+1F = 0 and FW + (−)W+1F ≠ 0 for 1 < W < K, where K is a fixed positive integer greater than 2. The case when K is odd (≥3) has been considered in this paper.
Lovejoy S. Das
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