The Ricci soliton condition reduces to a set of ODEs when one assumes that the metric is a doubly-warped product of a ray with a sphere and an Einstein manifold. If the Einstein manifold has positive Ricci curvature, we show there is a one-parameter family of solutions which give complete non-compact Ricci solitons.

Recently, the present authors considered doubly warped product CR-submanifolds in a locally conformal Kaehler manifold and got some inequalities about the length of the second fundamental form ([14]). In this report, we obtain an inequality of the mean curvature of a doubly warped product CR-submanifold in a locally conformal Kaehler space form. Then, we consider the equality case of this inequ...

The junction condition across a singular surface in general relativity, formulated by Israel, has double covariance. In this paper, a general perturbation scheme of the junction condition around an arbitrary background is given in a doubly covariant way. After that, as an application of the general scheme, we consider perturbation of the junction condition around a background with the symmetry ...

In the present paper we study the geometry of doubly extended Lie groups with their natural biinvariant metric. We describe the curvature, the holonomy and the space of parallel spinors. This is completely done for all simply connected groups with biinvariant metric of Lorentzian signature (1, n − 1), of signature (2, n − 2) and of signature (p, q), where p + q ≤ 6. Furthermore, some special se...

In this article, we obtain bounds for Ricci curvature doubly warped products pointwise bi-slant submanifolds in generalized complex space forms and discuss the equality case of inequality. We also derive non-existence such immersions. Finally, construct some applications result terms Harmonic function, Hessian tensor, Dirchilet energy function.

A bstract We examine holographic complexity in the doubly model introduced [1, 2] to study quantum extremal islands. focus on complexity=volume (CV) proposal for boundary subregions island phase. Exploiting Fefferman-Graham expansion of metric and other geometric quantities near brane, we derive leading contributions interpret these terms generalized volume derived from induced higher-curvature...

We report the observation of a doubly periodic surface defect pattern in the liquid crystal 8CB, formed during the nematic-smectic-A phase transition. The pattern results from the antagonistic alignment of the 8CB molecules, which is homeotropic at the surface and planar in the bulk of the sample cell. Within the continuum Landau-de Gennes theory of smectic liquid crystals, we find that the lon...

Orthogeodesic models admit marginal local cuts and therefore separate inference on subparameters is asymptotically justified. Doubly-flat orthogeodesic models admit local cuts marginally and conditionally. Two important empirical models for panel data are used to illustrate this property and demonstrate its usefulness. The relation to local ancillarity and local sufficiency is explored. An alte...

1. Flexible substrates can be subdivided in two classes: Substrates that allow for inextensial bending only and substrates that due to the larger stretchability allow for more arbitrary bending. The first group of flexible substrates can only be applied on surfaces with zero Gaussian curvature. The application of the second group of flexible substrates is more general. They can also be applied ...