We study the intrinsic geometry of hypersurfaces in Calabi-Yau manifolds of real dimension 6 and, more generally, SU(2)-structures on 5manifolds defined by a generalized Killing spinor. We prove that in the real analytic case, such a 5-manifold can be isometrically embedded as a hypersurface in a Calabi-Yau manifold in a natural way. We classify nilmanifolds carrying invariant structures of thi...

We study the intrinsic geometry of hypersurfaces in Calabi-Yau manifolds of real dimension 6 and, more generally, SU(2)-structures on 5-manifolds defined by a generalized Killing spinor. We prove that in the real analytic case, such a 5-manifold can be isometrically embedded as a hypersurface in a Calabi-Yau manifold in a natural way. We classify nilmanifolds carrying invariant structures of th...

In the present paper a global conformal invariant Y of a closed initial data set is constructed. A spacelike hypersurface in a Lorentzian spacetime naturally inherits from the spacetime metric a diierentiation D e , the so-called real Sen connection, which turns out to be determined completely by the initial data h ab and ab induced on , and coincides, in the case of vanishing second fundamenta...

For (2+2)–dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as nonholonomic deformations of the Levi–Civita connection. Such deformations and induced geometric/physical objects are completely determined by a prescribed metric ...

Here (the last paper in a series of eight) we end our presentation of the basics of a systematical approach to the differential geometry of smooth manifolds which uses the geometric algebras of multivector and extensors (fields) developed in previous papers. The theory of the Riemann and Ricci fields associated to a given geometric structure, i.e., a triple (M,γ, g) where M is a smooth manifold...

Considering a multi-dimensional q-oscillator invariant under the (non quantum) group U(n), we construct a q-deformed Levi-Civita epsilon tensor from the inner product states. The invariance of this q-epsilon tensor is shown to yield the quantum group SLq(n) and establishes the relationship of the U(n) invariant q-oscillator to quantum groups and quantum group related oscillators. Furthermore th...

I. Introduction-a quick historical survey of geodesic flows on negatively curved spaces. II. Preliminaries on Riemannian manifolds A. Riemannian metric and Riemannian volume element B. Levi Civita connection and covariant differentiation along curves C. Parallel translation of vectors along curves D. Curvature E. Geodesics and geodesic flow F. Riemannian exponential map and Jacobi vector fields...

In this note we briefly summarize the necessary tools from complex manifold theory in order to give an introduction to the basic results about Kähler and locally conformal Kähler manifolds. We look at many equivalent definitions of all three types of manifolds and examine in detail the parallels which arise in the theories. These parallels include the compatibility of metrics and fundamental 2-...

We develop both mathematical models and computational algorithms for variational denoising and restoration of nonflat image features. Nonflat image features are those that live on Riemannian manifolds, instead of on the Euclidean spaces. Familiar examples include the orientation feature (from optical flows or gradient flows) that lives on the unit circle S, the alignment feature (from fingerpri...

We show how the recently developed string-inspired, projectively invariant gravitational model Thomas-Whitehead gravity (TW gravity) naturally gives rise to a field acting as inflaton. In formulation of TW gravity, ${\mathcal{D}}_{ab}$ is introduced into projective connection components and related rank-two tensor ${\mathcal{P}}_{ab}$. Through dynamical action in terms curvature, ${\mathcal{P}}...