A counterexample to the rigidity conjecture for polyhedra
A diameter sphere theorem for mainfolds of positive Ricci curvature.
A Divergence Theorem for Finlser Metrics.
A Frankel type theorem for CR submanifolds of Sasakian manifolds
We prove a Frankel type theorem for submanifolds of Sasakian manifolds, under suitable hypotheses on the index of the scalar Levi forms determined by normal directions. From this theorem we derive some topological information about submanifolds of Sasakian space forms.
A Function Defined on an Even-dimensional Real Submanifold of a Hermitian Manifold
A general comparison theorem with applications to volume estimates for submanifolds
A general optimal inequality for arbitrary Riemannian submanifolds.
A geometric characterization of the orbits of s-representations.
A lower bound for the i-th total absolute curvature of an immersion
A non-immersion theorem for hyperbolic manifolds.
A non-immersion theorem for spaceforms.
A note on Chen's basic equality for submanifolds in a Sasakian space form.
A note on constant geodesic curvature curves on surfaces
A note on equichordal graphs
A note on -curvature planes.
A note on the first Betti number of submanifolds with nonnegative Ricci curvature in codimension two.
A note on the holomorphic invariants of Tian-Zhu.
A pinching theorem on complete submanifolds with parallel mean curvature vectors
Let M be an n-dimensional complete immersed submanifold with parallel mean curvature vectors in an (n+p)-dimensional Riemannian manifold N of constant curvature c > 0. Denote the square of length and the length of the trace of the second fundamental tensor of M by S and H, respectively. We prove that if S ≤ 1/(n-1) H² + 2c, n ≥ 4, or S ≤ 1/2 H² + min(2,(3p-3)/(2p-3))c, n = 3, then M is umbilical. This result generalizes the Okumura-Hasanis...
A pointwise inequality in submanifold theory
We obtain a pointwise inequality valid for all submanifolds of all real space forms with and with codimension two, relating its main scalar invariants, namely, its scalar curvature from the intrinsic geometry of , and its squared mean curvature and its scalar normal curvature from the extrinsic geometry of in .
A proof of the Chern-Lashof conjecture in dimensions greater than five.