Vladimir Slesar

Inequalities for the Casorati curvatures of slant submanifolds in quaternionic space forms

In this paper we prove two sharp inequalities that relate the normalized scalar curvature with the Casorati curvature for a slant submanifold in a quaternionic space form. Moreover, we show that in both cases, the equality at all points characterizes the invariantly quasi-umbilical submanifolds.

Hidden symmetries on toric Sasaki-Einstein spaces

We describe the construction of Killing-Yano tensors on toric Sasaki-Einstein manifolds. We use the fact that the metric cones of these spaces are Calabi-Yau manifolds. The description of the Calabi-Yau manifolds in terms of toric data, using the Delzant approach to toric geometries, allows us to find explicitly the complex coordinates and write down the Killing-Yano tensors. As a concrete example we present the complete set of special Killing forms on the five-dimensional homogeneous Sasaki-Einstein manifold T 1,1.

Special Killing forms on toric Sasaki?Einstein manifolds

In this paper we study the interplay between complex coordinates on the Calabi–Yau metric cone and the special Killing forms on the toric Sasaki–Einstein manifold. First, we give a procedure to locally construct the special Killing forms. Finally, we exemplify the general scheme in the case of the five-dimensional spaces, identifying the additional special Killing 2-forms which were previously obtained using a different method by Visinescu (2012 Mod. Phys. Lett. A 27 1250217).

TRANSVERSAL KILLING AND TWISTOR SPINORS ASSOCIATED TO THE BASIC DIRAC OPERATORS

We study the interplay between the basic Dirac operator and the transversal Killing and twistor spinors. In order to obtain results for the general Riemannian foliations with bundle-like metric, we consider transversal Killing spinors that appear as natural extension of the harmonic spinors associated with the basic Dirac operator. In the case of foliations with basic-harmonic mean curvature, it turns out that this type of spinors coincide with the standard definition. We obtain the corresponding version of classical results on closed Riemannian manifold with spin structure, and extending some previous results.

A note on transverse divergence and taut Riemannian foliations

Abstract In this note we give a characterization of taut Riemannian foliations using the transverse divergence. This result turns out to be a convenient tool in the case of some standard examples. Furthermore, we show that a classical tautness result of Haefliger can be obtained in our particular setting as a straightforward consequence. In the final part of the paper we obtain a tautness characterization for transversally oriented foliations with dense leaves.

Killing forms and toric Sasaki-Einstein spaces

The construction of the special Killing forms on toric Sasaki-Einstein manifolds is presented. This goal is achieved using the interplay between complex coordinates of the Calabi-Yau metric cone and the special Killing forms on the toric Sasaki-Einstein space. As a concrete example, we present the complete set of special Killing forms on the five-dimensional Einstein-Sasaki Yp,q spaces. It is pointed out the existence of two additional special Killing forms associated with the complex holomorphic volume form of Calabi-Yau cone manifold.