A new framework is developed to intrinsically analyze sparsely observed Riemannian functional data. It features four innovative components: a frame-independent covariance function, smooth vector bundle termed bundle, parallel transport and metric on the bundle. The introduced intrinsic function links estimation of structure smoothing problems that involve raw observations derived from data, whi...

We construct new explicit non-singular metrics that are complete on non-compact Riemannian 8-manifolds with holonomy Spin(7). One such metric, which we denote by A 8 , is complete and non-singular on R 8. The other complete metrics are defined on manifolds with the topology of the bundle of chiral spinors over S 4 , and are denoted by B + 8 , B − 8 and B 8. The metrics on B + 8 and B − 8 occur ...

We construct new explicit non-singular metrics that are complete on non-compact Riemannian 8-manifolds with holonomy Spin(7). One such metric, which we denote by A 8 , is complete and non-singular on R 8. The other complete metrics are defined on manifolds with the topology of the bundle of chiral spinors over S 4 , and are denoted by B + 8 , B − 8 and B 8. The metrics on B + 8 and B − 8 occur ...

A flat complex vector bundle (E, D) on a compact Riemannian manifold (X, g) is stable (resp. polystable) in the sense of Corlette [C] if it has no D-invariant subbundle (resp. if it is the D-invariant direct sum of stable subbundles). It has been shown in [C] that the polystability of (E, D) in this sense is equivalent to the existence of a so-called harmonic metric in E. In this paper we consi...

In a recent paper [Salimov, A., Asl, M.B., Kazimova, S.: Problems of lifts in symplectic geometry. Chin Ann. Math. Ser. B. 40(3), (2019), 321-330] the authors have investigated curious fact that canonıcal structure dp = dpi ∧ dxi on cotangent bundle may be given by introduction isomorphism between tangent and bundles. Our analysis began with observation complete lift from base manifold to its i...

The purpose of this study is to evaluate the curvature tensor and Ricci a P-Sasakian manifold with respect quarter-symmetric metric connection on tangent bundle TM. Certain results semisymmetric manifold, generalized recurrent manifolds, pseudo-symmetric manifolds TM are proved.

Abstract We analyze the “eigenbundle” (localization bundle) of certain Hilbert modules over bounded symmetric domains rank r , giving rise to complex-analytic fibre spaces which are stratified length $$r+1.$$ r + 1 . The fibres describe...

In this work we investigate a class of spherically symmetric metrics in multidimensional (MD) gravity. The metric ansatz which is used has off diagonal elements which leads to these solutions having “electric” and/or “magnetic” charges. The solutions examined here are either MD wormholes or infinite/finite flux tubes. It is found that the type of solution obtained depends crucially on the relat...