arXiv research

The paper studies a new structure on contact manifolds and its foliation properties.

The paper characterizes Sasakian manifolds using weak nearly Sasakian structures.

We carry on a systematic study of nearly Sasakian manifolds. We prove that any nearly Sasakian manifold admits two types of integrable distributions with totally geodesic leaves which are, respectively, Sasakian or $5$-dimensional nearly Sasakian manifolds. As a consequence, any nearly Sasakian manifold is a contact ma…

We prove that every nearly Sasakian manifold of dimension greater than five is Sasakian. This provides a new criterion for an almost contact metric manifold to be Sasakian. Moreover, we classify nearly cosymplectic manifolds of dimension greater than five.

We provide a new, self-contained and more conceptual proof of the result that an almost contact metric manifold of dimension greater than 5 is Sasakian if and only if it is nearly Sasakian.

Only the 6-sphere has constant curvature hypersurfaces in nearly Kähler manifolds.

Geometric flows study nearly parallel G2-structures on 3-Sasakian 7-manifolds.

New metric structures generalize Sasakian and cosymplectic structures, proving rigidity and finding conditions.

Study weak quasi contact metric manifolds to generalize K-contact and Sasakian manifolds criteria.

In this paper, we introduce and study a new class of CR-lightlike submanifold of an indefinite nearly Sasakian manifold, called Quasi Generalized Cauchy-Riemann (QGCR) lightlike submanifold. We give some characterization theorems for the existence of QGCR-lightlike submanifolds and finally derive necessary and sufficie…

The paper finds exact solutions to a complex Einstein-Dirac-Maxwell system on 4D Sasakian spacetimes.

In this expository article we discuss the relations between Sasakian geometry, reduced holonomy and supersymmetry. It is well known that the Riemannian manifolds other than the round spheres that admit real Killing spinors are precisely Sasaki-Einstein manifolds, 7-manifolds with a nearly parallel G2 structure, and nea…

New structures defined for studying contact foliations and their geometry.

Nearly $G_2$-structures are unstable under a modified $G_2$-Laplacian co-flow.

The concept of quasi generalized CR-lightlike was first introduced by the authors in [18]. In this paper, we focus on ascreen and co-screen quasi generalized CR-lightlike submanifolds of indefinite nearly $μ$-Sasakian manifold. We prove an existence theorem for minimal ascreen quasi generalized CR-lightlike submanifold…

Study explores weak generalized K-contact structures in contact metric spaces.

The study examines conditions for weak nearly cosymplectic manifolds to split into products.

Study 3-Sasakian and G2 structures on manifolds.

In this paper, we prove that the transverse Mabuchi K-energy functional is convex along the weak geodesic in the space of Sasakian metrics. As an application, we obtain the uniqueness of constant scalar curvature Sasakian metrics modulo automorphisms for the transverse holomorphic structure.

Study on a new type of manifolds that generalize almost C-manifolds.

In this paper, we study warped product submanifolds of nearly trans-Sasakian manifolds. The non-existence of the warped product semi-slant submanifolds of the type $N_θ\times{_{f}N_T}$ is shown, whereas some characterization and new geometric obstructions are obtained for the warped products of the type $N_T\times{_{f}…

Study of instantons on Stiefel manifold with $G_2$ and Sasakian structures.

First non-trivial examples of deformed G_2-instantons, distinguishing nearly parallel G_2-structures.

We introduce a new general class of metric f-manifolds which we call (nearly) trans-S-manifolds and includes S- manifolds, C-manifolds, s-th Sasakian manifolds and generalized Kenmotsu manifold studied previously. We prove their main properties and we present many examples which justify their study.

Researchers compute the ν-invariant for specific G2-structures on Aloff-Wallach spaces.

The study constructs associative 3-folds in squashed 3-Sasakian manifolds.

The paper explores generalized Riemannian manifolds with weak metric structures.

Study calibrated geometry in hyperkähler cones and their related spaces.

A geometry with parallel skew-symmetric torsion is a Riemannian manifold carrying a metric connection with parallel skew-symmetric torsion. Besides the trivial case of the Levi-Civita connection, geometries with non-vanishing parallel skew-symmetric torsion arise naturally in several geometric contexts, e.g. on natural…

We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds, nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifo…

For gauge groups $U(1)$ and $SO(3)$ we classify invariant $G_2$-instantons for homogeneous coclosed $G_2$-structures on Aloff-Wallach spaces $X_{k,l}$. As a consequence, we give examples where $G_2$-instantons can be used to distinguish between different strictly nearly parallel $G_2$-structures on the same Aloff-Walla…

We develop some pluripotential theoretic techniques for the transversally holomorphic foliation of a Sasakian manifold. We prove the convexity of the K-energy along weak geodesics for Sasakian manifolds. This implies that the K-energy is bounded below if a constant scalar curvature structure exists with those metrics m…

The study finds a continuous map achieving minmax area under Legendrian constraints.

We construct exact solutions of the Einstein-Dirac equation, which couples the gravitational field with an eigenspinor of the Dirac operator via the energy-momentum tensor. For this purpose we introduce a new field equation generalizing the notion of Killing spinors. The solutions of this spinorial field equation are c…

New methods lift weak supervision to structured prediction, providing robustness guarantees.

We study weakened $f$-structures on manifolds, generalizing classical results.

For any triple $(M^n, g, \nabla)$ consisting of a Riemannian manifold and a metric connection with skew-symmetric torsion we introduce an elliptic, second order operator $Ω$ acting on spinor fields. In case of a reductive space and its canonical connection our construction yields the Casimir operator of the isometry gr…

We study the spinorial Killing equation of supergravity involving a torsion 3-form $\T$ as well as a flux 4-form $\F$. In dimension seven, we construct explicit families of compact solutions out of 3-Sasakian geometries, nearly parallel $\G_2$-geometries and on the homogeneous Aloff-Wallach space. The constraint $\F \c…

Study curvature properties of w.a. S-manifolds with new conditions.

The paper explores new connections in non-symmetrical gravitational theory using weak metric structures.

Study immersions of Sasakian manifolds into Sasakian space forms.

New solutions found for G2 system on squashed manifolds.

Spinorially constructs Sasakian and 3-Sasakian structures in arbitrary dimensions.

The object of this paper is to study the invariant submanifolds of Sasakian generalized-Sasakian-space-form. Here, we obtain some equivalent conditions for an invariant submanifold of a Sasakian generalized-Sasakian-space-forms to be totally geodesic.

We show that the contact reduction can be specialized to Sasakian manifolds. We link this Sasakian reduction to Kähler reduction by considering the Kähler cone over a Sasakian manifold. We present examples of Sasakian manifolds obtained by $S^1$ reduction of standard Sasakian spheres.

Weak diffusion priors can still perform well in inverse problems.

Study classifies quasi-Sasakian 3-manifolds, linking them to Sasakian and co-Kähler structures.

For G_2-manifolds the Fernández-Gray class X_1+X_4 is shown to consist of the union of the class X_4 of G_2-manifolds locally conformal to parallel G_2-structures and that of conformal transformations of nearly parallel or weak holonomy G_2-manifolds of type X_1. The analogous conclusion is obtained for Gray-Hervella c…