Study isotropic Riemannian maps and helices along them.
problem Understanding Riemannian maps and their associated helices.
method Presented isotropic Riemannian maps and characterized helices along them.
result Characterization of helices along Riemannian maps.
This study examines Clairaut slant Riemannian maps from Riemannian to Kähler manifolds.
problem Characterizing Clairaut slant Riemannian maps between Riemannian and Kähler manifolds.
method Analyzing necessary and sufficient conditions for geodesics, Clairaut slant maps, total geodesy, integrability, and harmonicity.
result Obtained inequalities involving second fundamental forms of Clairaut slant Riemannian maps.
Paper defines and studies Clairaut warped product Riemannian maps.
problem Understanding the geometry of specific Riemannian maps.
method Identify geodesic conditions, derive conditions for Clairaut maps, and calculate curvature.
result Found conditions for a warped product Riemannian map to be Clairaut.
We introduce slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of slant immersions, invariant Riemannian maps and anti-invariant Riemannian maps. We give examples, obtain characterizations and investigate the harmonicity of such maps. We also obtain necessary and sufficie…
The paper explores geometric properties of Riemannian warped product maps and their curvature.
problem Investigating the geometric properties of Riemannian warped product maps.
method The approach involves establishing conditions for geodesics, deriving curvature tensors, and examining various types of maps.
result Derivation of integral formula for scalar curvature of conformal Riemannian warped product maps.
As a generalization of anti-invariant Riemannian submersions, we introduce anti-invariant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We give examples and investigate the geometry of foliations which are arisen from the definition of an anti-Riemannian map. Then we give a decomposition theo…
Harmonic maps studied in sub-Riemannian geometry for Lie groups.
problem Defining and characterizing harmonic maps in sub-Riemannian settings.
method Generalization of Riemannian harmonic maps to sub-Riemannian manifolds and Lie groups.
result Conditions for sub-Riemannian harmonic maps and their classification.
Study on Clairaut maps from nearly Kahler to Riemannian manifolds.
problem Characterizing Clairaut maps from nearly Kahler manifolds.
method Analyzing conditions for Clairaut maps to be totally geodesic foliations.
result Non-trivial examples of Clairaut maps are provided.
Establish generalized Chen inequalities for Riemannian submersions and Riemannian maps with applications.
problem Generalized Chen inequalities for Riemannian submersions and Riemannian maps.
method Employing generalized δ-invariants introduced by Chen.
result Optimal inequalities involving δ-invariants and extrinsic invariants.
The paper establishes new Casorati inequalities for various Riemannian maps and submersions.
problem Developing new inequalities for Riemannian maps and submersions.
method Using general forms of Casorati inequalities, the paper derives inequalities for specific Riemannian spaces.
result The paper provides new Casorati inequalities for Riemannian maps and submersions.
The paper constructs gluing maps for harmonic maps between Riemannian manifolds.
problem Constructing harmonic maps between Riemannian manifolds.
method Gluing construction of extended harmonic maps.
result Construction of gluing maps for harmonic maps under specific conditions.
We give necessary and sufficient conditions for Riemannian maps to be biharmonic. We also define pseudo umbilical Riemannian maps as a generalization of pseudo-umbilical submanifolds and show that such Riemannian maps put some restrictions on the base manifolds.
The paper studies Riemannian maps with Ricci soliton base manifolds.
problem Analyzing Riemannian maps with specific properties of base manifolds.
method Analyzing Riemannian curvature tensor, Ricci tensor, scalar curvature, and necessary conditions for Ricci soliton leaves.
result Necessary and sufficient conditions for harmonicity and biharmonicity of Riemannian maps.
In this paper, we consider critical maps of a horizontal energy functional for maps from a sub-Riemannian manifold to a Riemannian manifold. These critical maps are referred to as subelliptic harmonic maps. In terms of the subelliptic harmonic map heat flow, we investigate the existence problem for subelliptic harmonic…
Defines and studies Clairaut Riemannian maps between manifolds and Ricci solitons.
problem Characterizing and analyzing Clairaut Riemannian maps.
method Using geodesic curves, necessary and sufficient conditions for harmonicity and Clairaut maps are derived.
result Necessary conditions for various properties of Clairaut Riemannian maps are established.
Maps on Sasakian manifolds limit to sub-Riemannian distance bounds.
problem Understanding sub-Riemannian distances on Sasakian manifolds.
method Parallel and mirror maps along geodesics of a taming Riemannian metric.
result Limits of transport maps outside sub-Riemannian cut-locus provide bounds on sub-Riemannian distance.
Paper studies quaternionic space forms and Riemannian maps inequalities.
problem Investigate DDVV-type inequality for quaternionic space forms.
method Analyze Riemannian maps from quaternionic space forms to manifolds.
result Derived inequality with equality conditions discussed.
The paper studies bi-slant Riemannian maps to Kenmotsu manifolds and derives inequalities.
problem Investigating bi-slant Riemannian maps and their properties.
method Introducing and studying bi-slant Riemannian maps, deriving curvature relations and inequalities.
result Construction of Chen-Ricci inequalities, DDVV inequalities, and optimal inequalities involving Casorati curvatures.
As a generalization of holomorphic submersions, anti-invariant submersions and slant submersions, we introduce slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We give examples, obtain the existence conditions of slant Riemannian maps and investigate harmonicity of such maps. We also obtai…
The article defines and analyzes Clairaut anti-invariant maps between Riemannian and trans-Sasakian manifolds.
problem Characterizing Clairaut anti-invariant Riemannian maps between specific types of manifolds.
method Deriving conditions for Clairaut maps, discussing integrability, and establishing harmonicity.
result Necessary and sufficient conditions for Clairaut anti-invariant maps are derived.
Defines basic Albanese maps for foliated Riemannian manifolds.
problem No specific problem stated; focuses on new concept definition.
method Introduces basic Albanese map using basic 1-forms.
result Relates basic Albanese map to classical Albanese map.
Extends symphonic maps to bi-symphonic maps between Riemannian manifolds.
problem Defining and exploring new types of maps between Riemannian manifolds.
method Introduces bi-symphonic maps by analyzing the bi-energy functional.
result New types of maps (bi-symphonic) with associated bi-energy functional.
In this article we introduce conformal Riemannian morphisms. The idea of conformal Riemannian morphism generalizes the notions of an isometric immersion, a Riemannian submersion, an isometry, a Riemannian map and a conformal Riemannian map. We show that every injective conformal Riemannian morphism is an injective conf…
As a generalization of slant Riemannian maps (Sahin), semi-slant Riemannian maps (Park), almost h-slant submersions (Park 2012), and almost h-semi-slant submersions (Park 2011), we introduce the notion of almost h-semi-slant Riemannian maps from almost quaternionic Hermitian manifolds to Riemannian manifolds. We invest…
Study Clairaut semi-slant/hemi-slant maps to Kähler manifolds.
problem Understanding Riemannian maps between specific types of manifolds.
method Analyzing Clairaut semi-slant/hemi-slant maps to Kähler manifolds.
result New insights into the properties of these maps.
Symphonic maps on non-compact Riemannian manifolds are non-existent.
problem Existence of symphonic maps on compact or non-compact Riemannian manifolds
method Study of conformal vector fields and Ricci solitons
result No symphonic maps exist
In this paper, we introduce metallic maps between metallic Riemannian manifolds, provide an example and obtain certain conditions for such maps to be totally geodesic. We also give a sufficient condition for a map between metallic Riemannian manifolds to be harmonic map. Then we investigate the constancy of certain map…
The paper examines HM-tensional and HS-tensional maps between Riemannian manifolds.
problem Analyzing tension fields of maps between Riemannian manifolds.
method Investigating harmonic maps and harmonic sections as tension fields.
result Characterization and properties of HM-tensional and HS-tensional maps. The paper studies geodesic mappings in special Riemannian manifolds.
problem Investigating geodesic mappings in specific Riemannian manifolds.
method Proof of geodesic mappings properties and new results on geodesic mappings of various Riemannian manifolds.
result New results on geodesic mappings of quasi Einstein, Ricci recurrent, and Ricci symmetric manifolds.
The paper sets new bounds for Ricci-curvature in submersions and maps.
problem Establishing bounds for Ricci-curvature in submersions and maps.
method Developed upper and lower bounds for Ricci-curvature in submersions and maps, providing geometric characterizations.
result New bounds for Ricci-curvature in submersions and maps have been derived.
The paper investigates subelliptic harmonic maps with potential using heat flow.
problem Existence of subelliptic harmonic maps with potential under certain conditions.
method Investigates subelliptic harmonic maps with potential using a subelliptic heat flow.
result Proves existence results for subelliptic harmonic maps with potentials.
As a generalization of slant submersions (Sahin, 2011), semi-slant submersions (Park and Prasad), and slant Riemannian maps (Sahin), we define the notion of semi-slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We study the integrability of distributions, the geometry of fibers, the harmon…
The paper studies critical points of horizontal energy functional in Riemannian foliations.
problem Analyzing critical points of horizontal energy functional in Riemannian foliations.
method Utilizing stress-energy tensor, establishing monotonicity formulas, and Jin-type theorems.
result Established monotonicity formulas for horizontally harmonic maps and transversally harmonic maps.
Study uniquely determines Riemannian metric derivatives from boundary data.
problem Determining Riemannian metric derivatives from boundary data.
method Computing the full symbol of the elastic Dirichlet-to-Neumann map.
result The elastic Dirichlet-to-Neumann map uniquely determines all partial derivatives of the Riemannian metric on the boundary.
New exponential map for Lie groups connects to sub-Riemannian geometry.
problem Developing a new exponential map for Lie groups.
method Introducing a new exponential map related to sub-Riemannian geometry.
result New exponential map connects to sub-Riemannian geometry.
Study on stability of harmonic maps with sub-Riemannian geometry.
problem Stability of exponentially subelliptic harmonic maps.
method Derived first and second variation formulas, applied to prove stability under certain conditions.
result Exponentially subelliptic harmonic maps are stable if the target manifold has nonpositive curvature.
The paper derives Chen-Ricci inequalities for Riemannian submersions and maps.
problem Chen-Ricci inequalities for Riemannian submersions and maps.
method General forms of Chen-Ricci inequalities for Riemannian submersions and maps are derived, involving curvatures of subspaces.
result New, easy, and elegant techniques for Chen-Ricci inequalities are established.
Proves properties of sub-Riemannian exponential map, showing it's not injective.
problem Regularity and continuity of sub-Riemannian exponential map.
method Used sub-Riemannian Jacobi fields and Maslov index of Jacobi curves.
result Exponential map of 3D Heisenberg group is not injective near conjugate vectors.
Paper generalizes Schwarz lemma for harmonic maps between Riemannian manifolds.
problem Generalizing Schwarz lemma for harmonic maps.
method Using Bochner techniques and sub-Laplacian comparison theorem.
result Established a generalization of Schwarz lemma for transversally harmonic maps.
We introduce holomorphic Riemannian maps between almost Hermitian manifolds as a generalization of holomorphic submanifolds and holomorphic submersions, give examples and obtain a geometric characterization of harmonic holomorphic Riemannian maps from almost Hermitian manifolds to Kaehler manifolds.
Study on Riemannian submersions from nearly Kaehler manifolds.
problem Conditions for integrability and geodesic properties in Riemannian submersions.
method Investigation of various distributions and conditions for integrability and geodesic properties.
result Conditions for a generic Riemannian submersion to be a harmonic map.
The paper explores α−harmonic maps and their stability, proving key properties and conditions.
problem Existence and stability of α−harmonic maps between Riemannian manifolds. method Analysis of α−energy functional, construction of α−harmonic maps, and stability conditions. result Conditions for the stability of α−harmonic maps and their instability from compact manifolds. Gradient estimates for subelliptic harmonic maps with potential.
problem Estimating gradients of subelliptic harmonic maps.
method Investigation of subelliptic harmonic maps with potential from specific manifolds.
result Gradient estimates and Liouville type result established.
Study sesqui-harmonic map flow from Riemannian surfaces
problem Investigate sesqui-harmonic map flow from Riemannian surfaces
method L2-gradient flow of an energy functional
result Generalizes Struwe's regularity result for harmonic maps
The exponential map fails to be injective near critical points in sub-Riemannian geometry.
problem Injectivity failure of the exponential map at critical points in sub-Riemannian geometry.
method Analysis of the Hilbert invariant integral of the variational problem associated with the sub-Riemannian structure.
result Characterization of conjugate points in terms of metric structure.
The paper characterizes harmonic maps and studies their properties on Riemannian manifolds.
problem Characterizing and analyzing harmonic maps between Riemannian manifolds.
method Analytic and geometric methods, including L2-orthogonal decomposition and energy density analysis.
result A criterion for harmonic submersions and diffeomorphisms, and new results linking harmonic symmetric bilinear forms and metrics.
We consider harmonic maps into pseudo-Riemannian manifolds. We show the removability of isolated singularities for continuous maps, i.e. that any continuous map from an open subset of R^m into a pseudo-Riemannian manifold which is two times continuously differentiable and harmonic everywhere outside an isolated point i…
Notes on quasiregular maps between Riemannian manifolds, preserving Sobolev forms.
problem Extending quasiregular map theory from Euclidean to Riemannian manifolds.
method Recalling different approaches to first-order Sobolev spaces, showing equivalence, and transferring key theorems.
result Pull-backs with quasiregular maps preserve Sobolev differential forms of the conformal exponent.