A metric induced by the geometric interpretation of Rolle's theorem.
A metric inequality for the Thompson and Hilbert geometries.
A minimization problem arising from prescribing scalar curvature functions.
A model of gauge theory with invariant variables.
A Monge-Ampère equation in conformal geometry
We consider the Monge-Ampère-type equation , where is the Schouten tensor of a conformally related metric and is a suitably chosen constant. When the scalar curvature is non-positive we give necessary and sufficient conditions for the existence of solutions. When the scalar curvature is positive and the first Betti number of the manifold is non-zero we also establish existence. Moreover, by adapting a construction of Schoen, we show that solutions are in general not unique.
A monotonicity formula for Yang-Mills Fields.
A Morse theory for light rays on stably causal lorentzian manifolds
A Nakai-Moishezon criterion for non-Kähler surfaces
A version of the classical Nakai-Moishezon criterion is proved for all compact complex surfaces, regardless of the parity of the first Betti number.
A Narasimhan-Seshardri-Donaldson Correspondance over Non-orientable Surfaces.
A necessary and sufficient condition for a vector field to be Killing.
A new approach for describing instantaneous line congruence
Based on the E. Study’s map, a new approach describing instantaneous line congruence during the motion of the Darboux frame on a regular non-spherical and non-developable surface, whose parametric curves are lines of curvature, is proposed. Afterward, the pitch of general line congruence is developed and used for deriving necessary and sufficient condition for instantaneous line congruence to be normal. In terms of this, the derived line congruences and their differential geometric invariants were...
A new approach to the Ricci flow on
A New Approach to the Theory of the Riemann Space
A new characterization of Gromov hyperbolicity for negatively curved surfaces.
In this paper we show that to check Gromov hyperbolicity of any surface of constant negative curvature, or Riemann surface, we only need to verify the Rips condition on a very small class of triangles, namely, those obtained by marking three points in a simple closed geodesic. This result is, in fact, a new characterization of Gromov hyperbolicity for Riemann surfaces.
A new characterization of -stable hypersurfaces in space forms
In this paper we study the -stability of closed hypersurfaces with constant -th mean curvature in Riemannian manifolds of constant sectional curvature. In this setting, we obtain a characterization of the -stable ones through of the analysis of the first eigenvalue of an operator naturally attached to the -th mean curvature.
A new characterization of the sphere in
Let M be a closed connected surface in with positive Gaussian curvature K and let be the curvature of its second fundamental form. It is shown that M is a sphere if , for some constants c and r, where H is the mean curvature of M.
A new cohomology on special kinds of complex manifolds
A New Conformal Invariant and Its Applications to the Wilmore Conjecture and the First Eigenvalue of Compact Surfaces.
A new curvature invariant and entropy of geodesic flow.
A new definition of the circle by the use of bisectors