A basic inequality of submanifolds in quaternionic space forms.

Yoon, Dae Won

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Displaying similar documents to “A basic inequality of submanifolds in quaternionic space forms.”

A basic inequality for submanifolds in a cosymplectic space form.

Kim, Jeong-Sik, Choi, Jaedong (2003)

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An improved Chen-Ricci inequality for special slant submanifolds in Kenmotsu space forms

Simona Costache, Iuliana Zamfir (2014)

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B. Y. Chen [Arch. Math. (Basel) 74 (2000), 154-160] proved a geometrical inequality for Lagrangian submanifolds in complex space forms in terms of the Ricci curvature and the squared mean curvature. Recently, this Chen-Ricci inequality was improved in [Int. Electron. J. Geom. 2 (2009), 39-45]. On the other hand, K. Arslan et al. [Int. J. Math. Math. Sci. 29 (2002), 719-726] established a Chen-Ricci inequality for submanifolds, in particular in contact slant submanifolds,...

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A pointwise inequality in submanifold theory

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

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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 $n \geq 2$ 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 $N^{m} (c)$ .

Slant submanifolds with prescribed scalar curvature into cosymplectic space form.

Gupta, Ram Shankar, Haider, S.M.Khrusheed, Sharfuddin, A. (2006)

Balkan Journal of Geometry and its Applications (BJGA)

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A note on Chen's basic equality for submanifolds in a Sasakian space form.

Tripathi, Mukut Mani, Kim, Jeong-Sik, Kim, Seon-Bu (2003)

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Ricci and scalar curvatures of submanifolds of a conformal Sasakian space form

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We introduce a conformal Sasakian manifold and we find the inequality involving Ricci curvature and the squared mean curvature for semi-invariant, almost semi-invariant, $θ$ -slant, invariant and anti-invariant submanifolds tangent to the Reeb vector field and the equality cases are also discussed. Also the inequality involving scalar curvature and the squared mean curvature of some submanifolds of a conformal Sasakian space form are obtained.

Operator models and Arveson's curvature invariant

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