In the study of conformai geometry, the method of elliptic partial differential equations is playing an increasingly significant role. Since the solution of the Yamabe problem, a family of conformally covariant operators (for definition, see section 2) generalizing the conformai Laplacian, and their associated conformai invariants have been introduced. The conformally covariant powers of the La...

In the study of conformal geometry, the method of elliptic partial differential equations is playing an increasingly significant role. Since the solution of the Yamabe problem, a family of conformally covariant operators (for definition, see section 2) generalizing the conformal Laplacian, and their associated conformal invariants have been introduced. The conformally covariant powers of the La...

Estimating principal curvatures and principal directions of a smooth surface represented by a triangular mesh is an important step in many CAD or graphics related tasks. This paper presents a new method for curvature tensor estimation on a triangular mesh by replacing flat triangles with triangular parametric patches. An improved local interpolation scheme of cubic triangular Bézier patches to ...

Methods based on partial differential equations (PDEs) belong to those image processing techniques that can be extended in a particularly elegant way to tensor fields. In this survey paper the most important PDEs for discontinuity-preserving denoising of tensor fields are reviewed such that the underlying design principles becomes evident. We consider isotropic and anisotropic diffusion filters...

Riemannian geometry, based upon a metric form ds = gijdxdx', gives us the curvature tensor R)u as the sole basic differential invariant of the space, and of the symmetric tensor gy. The general tensor g^ can be broken up into the sum of two irreducible components, namely the symmetric and antisymmetric portions defined respectively by 2giij)=gij+gji and 2g[ij]=gij--gji. The latter disappears in...

In this article, normal paracontact metric space forms are investigated on W_0-curvature tensor. Characterizations of obtained Special curvature conditions established with the help Riemann, Ricci, concircular tensors discussed With these conditions, important characterizations obtained.

We generalize the construction of canonical algebraic curvature tensors by selfadjoint endomorphisms of a vector space to arbitrary endomorphisms. Provided certain basic rank requirements are met, we establish a converse of the classical fact that if A is symmetric, then RA is an algebraic curvature tensor. This allows us to establish a simultaneous diagonalization result in the event that thre...

For many design applications, where multiple primary surface pieces meet, the distribution of curvature is more important than formally achieving exact curvature continuity. For parametric spline surfaces, when constructing a multi-sided surface cap, we demonstrate a strong link between the uniform variation of the re-parameterization between (boundary) data of the joining pieces and a desirabl...

The aim of the present paper is to provide an intrinsic investigation of projective changes in Finlser geometry, following the pullback formalism. Various known local results are generalized and other new intrinsic results are obtained. Nontrivial characterizations of projective changes are given. The fundamental projectively invariant tensors, namely, the projective deviation tensor, the Weyl ...

A bstract We study the theory and phenomenology of massive spin-2 fields during inflation with nonzero background chemical potential, extend cosmological collider physics to tensor modes. identify a unique dimension-5 parity-violating potential operator for fields, which leads ghost-free linear propagating one scalar mode two The greatly boosts production even very heavy particles, thereby larg...