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...
A scalar geodesic deviation equation and a phase theorem.
A secondary Chern-Euler class.
A second-order identity for the Riemann tensor and applications
A second-order differential identity for the Riemann tensor is obtained on a manifold with a symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors are derived from it. Applications to manifolds with recurrent or symmetric structures are discussed. The new structure of K-recurrency naturally emerges from an invariance property of an old identity due to Lovelock.
A series of Kählerian invariants and their applications to Kählerian geometry.
A sharp four dimensional isoperimetric inequality.
A short note on -biharmonic hypersurfaces
In the present paper we give some properties of -biharmonic hypersurfaces in real space forms. By using the -biharmonic equation for a hypersurface of a Riemannian manifold, we characterize the -biharmonicity of constant mean curvature and totally umbilical hypersurfaces in a Riemannian manifold and, in particular, in a real space form. As an example, we consider -biharmonic vertical cylinders in .