arXiv research

Study on submanifolds in generalized Sasakian-space-forms with various connections.

Study invariant submanifolds in generalized Sasakian-space-forms.

Study finds conditions for Legendre curves to be interpolating sesqui-harmonic in Sasakian space forms.

We show that there is no phi-recurrent generalized Sasakian-space-forms, when is a non-zero constant.

Paper studies invariant submanifolds in Sasakian spaces, finding conditions for total geodesy.

Researchers provide explicit parametrizations for Sasakian space forms.

Study biharmonic hypersurfaces in Sasakian space form using Tanaka-Webster connection.

Sharp inequalities for submersions from Sasakian space forms.

In this paper, we show that a generalized Sasakian space form of dimension greater than three is either of constant sectional curvature; or a canal hypersurface in Euclidean or Minkowski spaces; or locally a certain type of twisted product of a real line and a flat almost Hermitian manifold; or locally a wapred product…

Study immersions of Sasakian manifolds into Sasakian space forms.

The study examines curvature tensors and solitons in Lorentzian trans-Sasakian space forms.

New types of null hypersurfaces found in Sasakian space-forms.

We classify all proper-biharmonic Legendre curves in a Sasakian space form and point out some of their geometric properties. Then we provide a method for constructing anti-invariant proper-biharmonic submanifolds in Sasakian space forms. Finally, using the Boothby-Wang fibration, we determine all proper-biharmonic Hopf…

We consider biharmonic submanifolds in both generalized complex and Sasakian space forms. After giving the biharmonicity conditions for submanifolds in these spaces, we study different particular cases for which we obtain curvature estimates. We consider curves, complex and Lagrangian surfaces and hypersurfaces for the…

Hyperbolic solitons on trans-Sasakian space forms and their submanifolds

We find the characterization of maximum dimensional proper-biharmonic integral $\mathcal{C}$-parallel submanifolds of a Sasakian space form and then classify such submanifolds in a 7-dimensional Sasakian space form. Working in the sphere $\mathbb{S}^7$ we explicitly find all 3-dimensional proper-biharmonic integral $C$…

Sasakian immersions prove Sasaki-Ricci solitons are η-Einstein with rational constants.

Study on submanifolds in specific geometric spaces.

In [5], D. Fetcu and C. Oniciuc presented the classification result for biharmonic $\mathcal{C}$-parallel Legendrian submanifolds in $7$-dimensional Sasakian space forms. However, it is incomplete. In this paper, all such submanifolds are explicitly determined.

We classify the biharmonic non-Legendre curves in a Sasakian space form for which the angle between the tangent vector field and the characteristic vector field is constant and obtain explicit examples of such curves in $\mathbb{R}^{2n+1}(-3)$.

The paper derives inequalities for Riemannian submersions and their applications.

The study examines biharmonic hypersurfaces in Sasakian space forms.

The paper establishes new Casorati inequalities for various Riemannian maps and submersions.

The paper characterizes Whitney and contact Whitney spheres in complex and Sasakian space forms.

We study the global geometry of surfaces in Sasakian space forms whose mean curvature vector is parallel in the normal bundle (these include the Riemannian Heisenberg space of dimension $2n+1$). We prove a codimension reduction theorem. We introduce two holomorphic quadratic differentials on anti-invariant such surface…

Study on curvature properties of N(κ)-contact metric manifolds with generalized Tanaka-Webster connection.

It is an interesting question whether a given equation of motion has a periodic solution or not, and in the positive case to describe them. We investigate periodic magnetic curves in elliptic Sasakian space forms and we obtain a quantization principle for periodic magnetic flowlines on Berger spheres. We give a criteri…

We classify the biharmonic Legendre curves in a Sasakian space form, and obtain their explicit parametric equations in the $(2n+1)$-dimensional unit sphere endowed with the canonical and deformed Sasakian structures defined by Tanno. Then, composing with the flow of the Reeb vector field, we transform a biharmonic inte…

Study of Sasakian immersions in Heisenberg group and $\mathbb{B}^N imes \mathbb{R}$, focusing on $η$-Einstein case.

We study f-biharmonic and bi-f-harmonic submanifolds in both generalized complex and Sasakian space forms. We prove necessary and sufficient condition for f-biharmonicity and bi-f-harmonicity in the general case and many particular cases. Some non-existence results are also obtained.

We obtain a basic inequality involving the Laplacian of the warping function and the squared mean curvature of any warped product isometrically immersed in a Riemannian manifold without assuming any restriction on the Riemann curvature tensor of the ambient manifold. Applying this general theory, we obtain basic inequa…

Using as an underlying manifold an alpha-Sasakian manifold we introduce warped product Kaehler manifolds. We prove that if the underlying manifold is an alpha-Sasakian space form, then the corresponding Kaehler manifold is of quasi-constant holomorphic sectional curvatures with special distribution. Conversely, we prov…

We present Chen-Ricci inequality and improved Chen-Ricci inequality for curvature like tensors. Applying our improved Chen-Ricci inequality we study Lagrangian and Kaehlerian slant submanifolds of complex space forms and C-totally real submanifolds of Sasakian space forms.

The study classifies CR solitons based on $C_0$-positivity and negativity.

We extend a result of Patodi for closed Riemannian manifolds to the context of closed contact manifolds by showing the condition that a manifold is an $η$-Einstein Sasakian manifold is spectrally determined. We also prove that the condition that a Sasakian space form has constant $φ$-sectional curvature $c$ is spectral…

Proves Frankel theorem for generic submanifolds in Sasakian manifolds.

The paper proves existence and eigenvalue bounds for CR structures, leading to uniformization theorems.

The paper investigates differential geometry of CR manifolds with new metrics.

The paper derives inequalities for Riemannian submersions and applies them to specific space forms.

Paper establishes new inequality for Riemannian maps and applies it to various space forms.

Local Sasaki-Ricci solitons are $η$-Einstein in certain fiber products of homogeneous Sasakian manifolds.

Study on special null submanifolds in indefinite Sasakian manifolds.

The orthogonal decomposition of the Webster curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differential inequalities from the Weitzenböck formulas for the traceless pseudo-Hermitian Ricci tensor and the Chern-Moser tensor of Sasakian manifol…

We prove that every Kaehler metric, whose potential is a function of the time-like distance in the flat Kaehler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local classification of the Kaehler manifolds with the above mentioned metrics. New examples o…

The paper derives Chen-Ricci inequalities for Riemannian submersions and maps.

This paper studies Sasakian quasi-Killing spinors on 3D Sasakian manifolds.

Paper defines generalized braids and proves their subgroup status.

Defines a new Poisson structure for generalized Sasakian spaces.