In this paper, we discuss the relationships between spaces with locally countable weak-bases and spaces with various locally countable networks, establish the relationships between spaces with locally countable weak-bases and locally separable metric spaces, and show that spaces have locally countable weak-bases if and only if they are locally Lindelöf, g-metrizable spaces. These are improvemen...

Abstract We show that every 3- $$(\alpha ,\delta )$$ ( α , δ ) -Sasaki manifold of dimension $$4n + 3$$ 4 n + 3 admits a locally defined Riemannian sub...

Let V be a noncompact complete Riemannian manifold. We find a geometric condition which assures that the essential spectrum of the Laplacian on V contains a half-line, by means of fiber bundle structures and the asymptotic behavior of mean curvatures on the ends of V , and give lower bounds of the essential spectrum. Our criteria can be applied to locally symmetric spaces of finite volume and m...

Let G be the group of points of a split reductive group over a finite extension of Qp. In this paper, we compute the dimensions of certain classes of locally analytic G-representations. This includes principal series representations and certain representations coming from homogeneous line bundles on p-adic symmetric spaces. As an application, we compute the dimensions of the unitary GL2pQpq-rep...

In many applications, the curvature of space supporting data makes statistical modeling challenging. this paper we discuss construction and use probability distributions wrapped around manifolds using exponential maps. These have already been used on specific manifolds. We describe their in unifying framework affine locally symmetric spaces. Affine spaces are a broad class containing encountere...