An equivalent flat condition.
An Equivariant Pniching Theorem.
An estimate of the pinching constant of minimal hypersurfaces with constant scalar curvature in the unit sphere.
An example of a 6-dimensional flat almost Hermitian manifold
An example of an asymptotically Chow unstable manifold with constant scalar curvature
Donaldson proved that if a polarized manifold has constant scalar curvature Kähler metrics in and its automorphism group is discrete, is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where is not discrete.
An example of Lie group with Sasakian structure of constant -sectional curvature.
An excess sphere theorem
An exhaustion of locally symmetric spaces by compact submanifolds with corners.
An existence result for minimal spheres in manifolds boundary
We prove the existence of a not homotopically trivial minimal sphere in a 3-manifold with boundary, obtained by deleting an open connected subset from a compact Riemannian oriented 3-manifold with boundary, having trivial second homotopy group.
An Existence Theorem for Harmonic Maps.
An existence theorem for the Yamabe problem on manifolds with boundary
Let be a compact Riemannian manifold with boundary. We consider the problem (first studied by Escobar in 1992) of finding a conformal metric with constant scalar curvature in the interior and zero mean curvature on the boundary. Using a local test function construction, we are able to settle most cases left open by Escobar’s work. Moreover, we reduce the remaining cases to the positive mass theorem.
An explicit classification of 3-dimensional Riemannian spaces satisfying
An explicite description of harmonic measure.
An extension of a flat Koszul connection being a Maurer-Cartan form.
An extension of a result of H. Hopf to Kähler submanifolds of
An Extension of Calabi's Rigidity theorem to complex submanifolds of indefinite complex space forms.
An Extrinsic Rigity Theorem for Minimal Surfaces in S3.
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