arXiv research

Study f-biharmonic maps and submanifolds, proving rigidity and classifications.

f-Biharmonic maps are the extrema of the f-bienergy functional. f-biharmonic submanifolds are submanifolds whose defining isometric immersions are f-biharmonic maps. In this paper, we prove that an f-biharmonic map from a compact Riemannian manifold into a non-positively curved manifold with constant f-bienergy density…

Study f-biharmonic and bi-f-harmonic submanifolds in complex and Sasakian space forms.

The paper studies $f$-biharmonic maps and submersions in space forms.

Study of $f$-biharmonic hypersurfaces in conformally flat spaces.

The paper defines and analyzes $f$-biharmonic $θ_{α}$-slant curves in $\mathcal{S}$-space forms.

We study biharmonic maps and f-biharmonic maps from a round sphere $(S^2, g_0)$, the latter maps are equivalent to biharmonic maps from Riemann spheres $(S^2, f^{-1}g_0)$. We proved that for rotationally symmetric maps between rotationally symmetric spaces, both biharmonicity and f-biharmonicity reduce to a 2nd order l…

The paper shows bi-f-harmonic and f-biharmonic maps are equivalent and explores their properties.

Proves generalized Chen's conjecture for biharmonic maps on foliations.

Both bi-harmonic map and $f$-harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study $f$-bi-harmonic maps as the critical points of the $f$-bi-energy functional $\frac{1}{2}\int_M f|τ(φ)|^2dv_{g}$. This class of maps generalizes both …

The paper studies $f$-polyharmonic maps and their properties.

This paper surveys parallel submanifolds in Riemannian and pseudo-Riemannian manifolds.

The study characterizes submanifolds in product spaces.

Researchers describe a specific type of submanifolds in Euclidean space.

Study on hemi-slant submanifolds in nearly Kaehler manifolds.

The paper finds many infinite-dimensional weakly reflective PF submanifolds in Hilbert spaces.

We introduce the notions of pointwise almost h-slant submanifolds and pointwise almost h-semi-slant submanifolds as a generalization of slant submanifolds, pointwise slant submanifolds, semi-slant submanifolds, and pointwise semi-slant submanifolds. We have characterizations and investigate the integrability of distrib…

Study of warped product pointwise bi-slant submanifolds in Kaehler manifolds.

The study explores properties of slant and semi-slant submanifolds in metallic Riemannian manifolds.

Study lightlike submanifolds in indefinite statistical manifolds, finding conditions and curvature expressions.

Develops methods for computing conformal invariants of submanifolds.

The paper introduces austere and arid submanifolds in Hilbert spaces.

Sphere theorems for submanifolds in Kähler and Sasaki spaces.

Study of CR-submanifolds in various Lorentzian manifolds.

Study attached submanifolds in solvmanifolds, generalizing symmetric space results.

Study properties of hemi-slant submanifolds in metallic Riemannian manifolds.

The paper derives Chen inequalities for statistical submanifolds in cosymplectic manifolds.

Survey of recent austere submanifold results.

Study on null submanifolds in indefinite complex contact geometry.

Study on deforming calibrated submanifolds with boundary constraints.

Minimal real Kähler submanifolds in codimension 6 are holomorphic.

Study on submanifolds in metallic Riemannian manifolds.

Integral coisotropic submanifolds are rigid and unobstructed in contact geometry.

Introduces new lightlike submanifolds in indefinite Kaehler manifolds.

Study various submanifolds in quaternionic skew-Hermitian spaces.

The paper studies biharmonic submanifolds in pseudo-Riemannian manifolds.

An n-dimensional submanifold X of a projective space P^N (C) is called tangentially degenerate if the rank of its Gauss mapping γ: X ---> G (n, N) satisfies 0 < rank γ< n. The authors systematically study the geometry of tangentially degenerate submanifolds of a projective space $P^N (\mathbf{C})$. By means of the foca…

Proves Frankel theorem for generic submanifolds in Sasakian manifolds.

The paper normalizes Poisson saturation of coregular submanifolds.

The paper studies $λ$-submanifolds in Gauss spaces and proves theorems for complete proper ones.

Study on special null submanifolds in indefinite Sasakian manifolds.

Study on submanifolds of Euclidean space, classifying their symmetry types.

In this paper, invariant submanifolds of a generalized Kenmotsu manifold are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be an invariant submanifold.In this case, we investigate further properties of invariant submanifolds of \ a generalized Kenmotsu man…

Study on biwarped product submanifolds in Kähler manifolds, proving their existence and characterizing them.

Recent developments on biconservative submanifolds in Riemannian geometry.

Constructs biharmonic and $r$-harmonic submanifolds in cohomogeneity one manifolds.

The paper studies a new type of submanifolds in product spaces.

Uniqueness and stability of minimal submanifolds proved.