A proof of Weinstein’s conjecture in
A Rigidity Theorem for Higher Codimensions.
A series of Kählerian invariants and their applications to Kählerian geometry.
A Sphere Theorem for Submanifolds in a Manifold with Pinched Positive Curvature.
A Sufficient Condition for a Compact Immersion to be Spherical.
A survey on axioms of submanifolds in Riemannian and Kaehlerian geometry
A Useful Characterization of Some Real Hypersurfaces in a Nonflat Complex Space Form
We characterize totally η-umbilic real hypersurfaces in a nonflat complex space form M̃ₙ(c) (= ℂPⁿ(c) or ℂHⁿ(c)) and a real hypersurface of type (A₂) of radius π/(2√c) in ℂPⁿ(c) by observing the shape of some geodesics on those real hypersurfaces as curves in the ambient manifolds (Theorems 1 and 2).
Almost complex surfaces in the nearly Kähler .
Almost cosymplectic real hypersurfaces in Kähler manifolds
Almost invariant submanifolds for compact group actions
We define a distance between submanifolds of a riemannian manifold and show that, if a compact submanifold is not moved too much under the isometric action of a compact group , there is a -invariant submanifold -close to . The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney’s idea of realizing submanifolds as zeros of sections...
An Arzela-Ascoli theorem for immersed submanifolds
The classical Arzela-Ascoli theorem is a compactness result for families of functions depending on bounds on the derivatives of the functions, and is of invaluable use in many fields of mathematics. In this paper, inspired by a result of Corlette, we prove an analogous compactness result for families of immersed submanifolds which depends only on bounds on the derivatives of the second fundamental forms of these submanifolds. We then show how the result of Corlette may be obtained as an immediate...
An equichordal characterization of round spheres.
An equivalence theorem for submanifolds of higher codimensions
For a submanifold of of any codimension the notion of type number is introduced. Under the assumption that the type number is greater than 1 an equivalence theorem is proved.
An Extension of Calabi's Rigidity theorem to complex submanifolds of indefinite complex space forms.
An improved Chen-Ricci inequality for special slant submanifolds in Kenmotsu space forms
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, in Kenmotsu...
An Inequality between the Exterior Diameter and the Mean Curvature of Bounded Immersions.
An inequality for totally real surfaces in complex space forms
An integral formula for closed surfaces and a generalization of -theorem
An integral formula for submanifolds and its application
An integral formula in differential geometry via mixed exterior algebra.