Displaying similar documents to “On Ricci curvature of totally real submanifolds in a quaternion projective space”

On minimal generic submanifolds immersed in S 2 m + 1

Masahiro Kon (2001)

Colloquium Mathematicae

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We give a pinching theorem for a compact minimal generic submanifold with flat normal connection immersed in an odd-dimensional sphere with standard Sasakian structure.

A pointwise inequality in submanifold theory

P. J. De Smet, F. Dillen, Leopold C. A. Verstraelen, L. Vrancken (1999)

Archivum Mathematicum

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We obtain a pointwise inequality valid for all submanifolds M n of all real space forms N n + 2 ( c ) with n ≥ 2 and with codimension two, relating its main scalar invariants, namely, its scalar curvature from the intrinsic geometry of M n , and its squared mean curvature and its scalar normal curvature from the extrinsic geometry of M n in N m ( c ) .

On Deszcz symmetries of Wintgen ideal submanifolds

Miroslava Petrović-Torgašev, Leopold C. A. Verstraelen (2008)

Archivum Mathematicum

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It was conjectured in [26] that, for all submanifolds M n of all real space forms M ˜ n + m ( c ) , the Wintgen inequality ρ ≤ H 2 - ρ ⊥ + c is valid at all points of M , whereby ρ is the normalised scalar curvature of the Riemannian manifold M and H 2 , respectively ρ ⊥ , are the squared mean curvature and the normalised scalar normal curvature of the submanifold M in the ambient space M ˜ , and this conjecture was shown there to be true whenever codimension m = 2 . For a given Riemannian manifold M , this inequality can be interpreted...