相关论文: Equivariant isospectrality and Sunada's Method

We construct a pair of compact, eight-dimensional, two-step Riemannian nilmanifolds $M$ and $M'$ which are isospectral for the Laplace operator on functions and such that $M$ has completely integrable geodesic flow in the sense of…

We construct examples of (effective) closed orbifolds which are covered by manifolds, but not finitely so.

We give a natural construction and a direct proof of the Adams isomorphism for equivariant orthogonal spectra. More precisely, for any finite group G, any normal subgroup N of G, and any orthogonal G-spectrum X, we construct a natural map A…

We are interested in the geometry of the group $\mathcal{D}_q(M)$ of diffeomorphisms preserving a contact form $\theta$ on a manifold $M$. We define a Riemannian metric on $\mathcal{D}_q(M)$, compute the corresponding geodesic equation, and…

In this paper, we introduce the notion of a regularizable submanifold in a Riemannian Hilbert manifold. This submanifold is defined as a curvature-invariant submanifold such that its shape operators and its normal Jacobi operators are…

We use correspondences to define a purely topological equivariant bivariant K-theory for spaces with a proper groupoid action. Our notion of correspondence differs slightly from that of Connes and Skandalis. We replace smooth K-oriented…

In a previous work, we studied isoparametric functions on Riemannian manifolds, especially on exotic spheres. One result there says that, in the family of isoparametric hypersurfaces of a closed Riemannian manifold, there exist at least one…

We construct spectral triples in a sense of noncommutative differential geometry, associated with a Riemannian foliation on a compact manifold, and describe its dimension spectrum.

Real smooth three-dimensional or higher Banach spaces are isomorphic with respect to the nonlinear structure of Birkhoff-James orthogonality if and only if they are isometrically isomorphic. Moreover, using smooth Radon planes and…

We construct a contractive, idempotent, MASA bimodule map on B(H), whose range is not a ternary subalgebra of B(H). Our method uses a crossed-product to reduce the existence of such an idempotent map to an analogous problem about the ranges…

The space of all non degenerate bilinear structures on a manifold $M$ carries a one parameter family of pseudo Riemannian metrics. We determine the geodesic equation, covariant derivative, curvature, and we solve the geodesic equation…

For an orbifold X which is the quotient of a manifold Y by a finite group G we construct a noncommutative ring with an action of G such that the orbifold cohomology of X as defined in math.AG/0004129 by Chen and Ruan is the G invariant…

In this paper, invariant submanifolds of a generalized Kenmotsu manifold are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be an invariant submanifold.In this case, we…

We consider the orthonormal frame bundle F(M) of a Riemannian manifold M. A construction of Sasaki defines a canonical Riemannian metric on F(M). We prove that for two closed Riemannian n-manifolds M and N, the frame bundles F(M) and F(N)…

For an orbifold, there is a notion of an orbifold embedding, which is more general than the one of sub-orbifolds. We develop several properties of orbifold embeddings. In the case of translation groupoids, we show that such a notion is…

In this paper, we introduce bi-slant Riemannian maps from Riemannian manifolds to Kenmotsu manifolds, which are the natural generalizations of invariant, anti-invariant, semi-invariant, slant, semi-slant and hemi-slant Riemannian maps, with…

Using standard methods for studying singularities of projections and of contacts, we classify the stable singularities of affine $\lambda$-equidistants of $n$-dimensional closed submanifolds of $\mathbb R^q$, for $q\leq 2n$, whenever…

We study the existence of closed geodesics on compact Riemannian orbifolds, and on noncompact Riemannian manifolds in the presence of a cocompact, isometric group action. We show that every noncontractible Riemannian manifold which admits…

This note pertains to isometric embeddings endowed with certain geometric properties. We study two embedding problems for a Riemannian manifold $M$ which is diffeomorphic to $\RR^n$ and admits a Bieberbach group $\Gamma$ acting by…

In a complete Riemannian manifold $(M, g)$ if the hessian of a real valued function satisfies some suitable conditions then it restricts the geometry of $(M, g)$. In this paper we characterize all compact rank-1 symmetric spaces, as those…