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Gabriel Eduard Vilcu

Publications and source records attributed to Gabriel Eduard Vilcu.

17 recordsLinked to original sources
arXiv2015

Toric data, Killing forms and complete integrability of geodesics in Sasaki-Einstein spaces $Y^{p,q}$

In the present paper we show that the complete list of special Killing forms on the 5-dimensional Sasaki-Einstein spaces $Y^{p,q}$ can be extracted using the symplectic potential and the classical Delzant construction. The results achieved here agree with previous ones obtained by direct computation, proving the reliability of the method which stands in fact as a general algorithm for toric Sasaki-Einstein manifolds. Finally, we discuss the integrability of geodesic motion in $Y^{p,q}$ spaces.

math-ph↗
arXiv2015

Toric data and Killing forms on homogeneous Sasaki-Einstein manifold $T^{1,1}$

Throughout this paper we investigate the complex structure of the conifold $C(T^{1,1})$ basically making use of the interplay between symplectic and complex approaches of the Kähler toric manifolds. The description of the Calabi-Yau manifold $C(T^{1,1})$ using toric data allows us to write explicitly the complex coordinates and apply standard methods for extracting special Killing forms on the base manifold. As an outcome, we obtain the complete set of special Killing forms on the five-dimensional Sasaki-Einstein space $T^{1,1}$.

math-ph↗
arXiv2014

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. In the general case we give a procedure to locally construct the special Killing forms. In the final part we exemplify the general scheme in the case of the $5-$dimensional $Y^{p,q}$ spaces, identifying the additional special Killing 2-forms which were previously obtained by the second author of the present paper, but with a different method, in [Mod. Phys. Lett. A 27 (2012) 1250217].

math-ph↗
arXiv2013

Geometric classifications of homogeneous production functions

In this paper, we completely classify homogeneous production functions with an arbitrary number of inputs whose production hypersurfaces are flat. As an immediate consequence, we obtain a complete classification of homogeneous production functions with two inputs whose production surfaces are developable.

math.DG↗
arXiv2012

Hidden Symmetries of Euclideanised Kerr-NUT-(A)dS Metrics in Certain Scaling Limits

The hidden symmetries of higher dimensional Kerr-NUT-(A)dS metrics are investigated. In certain scaling limits these metrics are related to the Einstein-Sasaki ones. The complete set of Killing-Yano tensors of the Einstein-Sasaki spaces are presented. For this purpose the Killing forms of the Calabi-Yau cone over the Einstein-Sasaki manifold are constructed. Two new Killing forms on Einstein-Sasaki manifolds are identified associated with the complex volume form of the cone manifolds. Finally the Killing forms on mixed 3-Sasaki manifolds are briefly described.

hep-th↗
arXiv2011

Slant submanifolds of quaternionic space forms

In this paper we establish some inequalities concerning the $k$-Ricci curvature of a slant submanifold in a quaternionic space form. We also obtain obstructions to the existence of quaternionic slant immersions in quaternionic space forms with unfull first normal bundle.

math.DG↗
arXiv2011

3-submersions from QR-hypersurfaces of quaternionic Kaehler manifolds

In this paper we study 3-submersions from a QR-hypersurface of a quaternionic Kaehler manifold onto an almost quaternionic hermitian manifold. We also prove the non-existence of quaternionic submersions between quaternionic Kaehler manifolds which are not locally hyper-Kaehler.

math.DG↗
arXiv2010

Submanifolds in manifolds with metric mixed 3-structures

Mixed 3-structures are odd-dimensional analogues of paraquaternionic structures. They appear naturally on lightlike hypersurfaces of almost paraquaternionic hermitian manifolds. We study invariant and anti-invariant submanifolds in a manifold endowed with a mixed 3-structure and a compatible (semi-Riemannian) metric. Particular attention is given to two cases of ambient space: mixed 3-Sasakian and mixed 3-cosymplectic.

math.DG↗
arXiv2004

Lightlike real hypersurfaces of paraquaternionic manifolds

The main purpose of this paper is to give fundamental properties of real lightlike hypersurfaces of paraquaternionic manifolds and to prove the non-existence of real lightlike hypersurfaces in paraquaternionic space forms under some conditions.

math.DG↗