A remark about minimal surfaces with flat embedded ends.
A remark on algebraic identities for the covariant derivative of the curvature tensor
A remark on almost umbilical hypersurfaces
In this article, we prove new stability results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almost umbilical hypersurfaces.
A remark on compact symplectic manifolds not admitting complex structures
A remark on four-dimensional almost Kähler-Einstein manifolds with negative scalar curvature.
A remark on mixed curvature measures for sets with positive reach.
A remark on natural quantum Lagrangians and natural generalized Schrödinger operators in Galilei quantum mechanics
A remark on semi-∇-flat functions
We give a pointwise characterization of semi-∇-flat functions on an affine manifold (M,∇).
A remark on the -splitting conjecture
A remark on the differential equations on the sphere
A remark on the topology of higher order frames
A remarkable transformation group on cotangent bundle.
A representation of the coalgebra of derivations for smooth spaces
Let be a field. The generalized Leibniz rule for higher derivations suggests the definition of a coalgebra for any positive integer . This is spanned over by , and has comultiplication and counit defined by and (Kronecker’s delta) for any . This note presents a representation of the coalgebra by using smooth spaces and a procedure of microlocalization. The author gives an interpretation of this result following the principles of the quantum theory of geometric spaces.
A Ricci flat pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold
We consider a certain pseudo-Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g) and obtain necessary and sufficient conditions for the pseudo-Riemannian manifold (TM,G) to be Ricci flat (see Theorem 2).
A Riemann-Lagrange geometrization for metrical multi-time Lagrange spaces.
A Riemann-Roch-Hirzebruch formula for traces of differential operators
Let be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an -dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, giving the Lefschetz number of as the integral over the manifold of a differential form. The class of this differential form is obtained via formal differential geometry from the canonical generator of the Hochschild cohomology of the algebra of differential operators on a formal neighbourhood of a...
A rigidity property of class VIIo surface fundamental groups.
A Rigidity Theorem for Higher Codimensions.
A rigidity theorem for Riemann's minimal surfaces
We describe first the analytic structure of Riemann’s examples of singly-periodic minimal surfaces; we also characterize them as extensions of minimal annuli bounded by parallel straight lines between parallel planes. We then prove their uniqueness as solutions of the perturbed problem of a punctured annulus, and we present standard methods for determining finite total curvature periodic minimal surfaces and solving the period problems.
A rough curvature-dimension condition for metric measure spaces
We introduce and study a rough (approximate) curvature-dimension condition for metric measure spaces, applicable especially in the framework of discrete spaces and graphs. This condition extends the one introduced by Karl-Theodor Sturm, in his 2006 article On the geometry of metric measure spaces II, to a larger class of (possibly non-geodesic) metric measure spaces. The rough curvature-dimension condition is stable under an appropriate notion of convergence, and stable under discretizations as...