Totally real submanifolds of ?P n satisfying a basic equality

Chen, B. Y.; Dillen, Franki; Verstraelen, Leopold; Vrancken, Luc

doi:10.1007/bf01202073

Cited by 54 publications

(58 citation statements)

References 5 publications

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“…, be a C-totally real submanifold of a Sasakian space form M 2m+ \c) which satisfies Chen's equality (4). Then for all X tangent to M", 4>X is perpendicular to H.…”

Section: Submanifolds With Maximal Dimensionmentioning

confidence: 99%

“…The warping functions can be determined from the equations (6), but we do not need explicit calculations. As the decomposition of S 2 "" 1 "' into a warped product whose first factor is 1-dimensional is unique up to isometries (see [5]), following a similar argument as in [4], we can assume that P\ = cos/, P2 = sin?.…”

Section: Proposition 5 Let M" Be An N-dimensional (N > 2) Minimal C-mentioning

confidence: 99%

“…In [6] a similar inequality for 8 M was established for totally real submanifolds of a complex space form; [6] and [4] contain also a classification of certain such submanifolds satisfying the equality.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A class of C-totally real submanifolds of Sasakian space forms

Defever¹,

Iordache²,

Verstraelen

1998

J Aust Math Soc A

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Recently, Chen defined an invariant &M of a Riemannian manifold M. Sharp inequalities for this Riemannian invariant were obtained for submanifolds in real, complex and Sasakian space forms, in terms of their mean curvature. In the present paper, we investigate certain C-totally real submanifolds of a Sasakian space form M 2m+ \c) satisfying Chen's equality.1991 Mathematics subject classification (Amer. Math. Soc): 53C15, 53C40, 53C25.

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“…, be a C-totally real submanifold of a Sasakian space form M 2m+ \c) which satisfies Chen's equality (4). Then for all X tangent to M", 4>X is perpendicular to H.…”

Section: Submanifolds With Maximal Dimensionmentioning

confidence: 99%

Section: Proposition 5 Let M" Be An N-dimensional (N > 2) Minimal C-mentioning

confidence: 99%

See 1 more Smart Citation

A class of C-totally real submanifolds of Sasakian space forms

Defever¹,

Iordache²,

Verstraelen

1998

J Aust Math Soc A

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“…Verstraelen and L. Vrancken showed in [5] that every totally real submanifold M of real dimension n in a complex space form M (c) of real dimension 2m satisfies Chen's inequality…”

mentioning

confidence: 99%

“…1. B. Y. Chen, F. Dillen, L. Verstraelen and L. Vrancken showed in [5] that every Lagrangian submanifold, of real dimension 2n, n ≥ 3, of a complex space form M (c), satisfying the equality…”

mentioning

confidence: 99%

Chen's inequality in the Lagrangian case

Oprea

2007

Colloq. Math.

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Abstract. In the theory of submanifolds, the following problem is fundamental: establish simple relationships between the main intrinsic invariants and the main extrinsic invariants of submanifolds. The basic relationships discovered until now are inequalities.To analyze such problems, we follow the idea of C. Udrişte that the method of constrained extremum is a natural way to prove geometric inequalities. We improve Chen's inequality which characterizes a totally real submanifold of a complex space form. For that we suppose that the submanifold is Lagrangian and we formulate and analyze a suitable constrained extremum problem.

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