The paper defines and explores Clairaut conformal submersions in Riemannian geometry.
problem Defining and characterizing Clairaut conformal submersions.
method Analyzing necessary and sufficient conditions, deriving geometric properties, and providing examples.
result Clairaut conformal submersions have constant dilation along fibers and are harmonic.
The paper characterizes Clairaut conformal submersions on Ricci solitons.
problem Characterizing Clairaut conformal submersions on Ricci solitons.
method Calculating scalar and Ricci tensors, providing necessary conditions for fibres and base manifolds to be Ricci solitons and Einstein, and solving Poisson equations.
result Necessary and sufficient conditions for Clairaut conformal submersions to be harmonic.
Study Clairaut anti-invariant submersions on nearly Kaehler manifolds.
problem Characterize geometric properties of Clairaut anti-invariant submersions.
method Investigate conditions for total geodesic maps and totally umbilical fibers.
result Conditions for Clairaut anti-invariant submersions to be totally geodesic.
We investigate new Clairaut conditions for anti-invariant submersions from normal almost contact metric manifolds onto Riemannian manifolds. We prove that there is no Clairaut anti-invariant submersion admitting vertical Reeb vector field when the total manifold is Sasakian. Several illustrative examples are also inclu…
The paper introduces and studies a new type of submersion in Riemannian geometry.
problem Exploring new submersions in Riemannian geometry.
method Defining and studying Clairaut Riemannian warped product submersions.
result Established conditions for a Riemannian warped product submersion to satisfy the Clairaut condition.
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.
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.
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.
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.
The paper studies Clairaut maps on Sasakian manifolds.
problem Investigating Clairaut maps on Sasakian manifolds.
method Analyzing necessary and sufficient conditions for geodesics and biharmonicity.
result Conditions for Clairaut anti-invariant Riemannian maps on Sasakian manifolds.
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.
The paper applies Clairaut's theorem to rotational surfaces in pseudo-Euclidean 4-space.
problem Exploring geodesic curves on rotational surfaces in pseudo-Euclidean 4-space.
method Expressing Clairaut's theorem and deriving equations for geodesic curves.
result Characterization of geodesic curves on hyperbolic and elliptic surfaces of rotation.
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.
Fermat constants fail to fully identify Clairaut constants for certain geodesics on a surface of revolution.
problem Identifying Clairaut constants from Fermat constants for specific geodesics.
method Analytical proof for a specific class of geodesics on a surface of revolution.
result Fermat constants do not fully determine Clairaut constants for some geodesics, except for a standard sphere.
The article generalizes Clairaut's formula for geodesics on submanifolds.
problem Conditions for geodesics on specific submanifolds.
method Study of geodesics on submanifolds involving Euclidean distance.
result Generalization of Clairaut's formula for higher dimensions.
Investigates physical properties on surfaces of rotation using Clairaut's theorem.
problem Understanding specific energy and angular momentum on surfaces of rotation.
method Used Clairaut's theorem with geodesic conditions to derive specific energy and angular momentum.
result Physical expressions for specific energy and angular momentum on surfaces of rotation were derived.
Study Clairaut maps on Kähler manifolds with Ricci solitons, finding curvature and scalar relations.
problem Exploring Clairaut maps on Kähler manifolds with Ricci solitons.
method Analyzing curvature relations, calculating Ricci tensor, and finding conditions for Einstein spaces.
result Conditions for range and kernel spaces to be Einstein and finding scalar curvature for range space.
The paper studies maps between Riemannian and Kähler manifolds, focusing on Clairaut semi-invariant Riemannian maps.
problem Analyzing maps between Riemannian and Kähler manifolds, particularly Clairaut semi-invariant Riemannian maps.
method Recalled and defined Clairaut semi-invariant Riemannian maps, derived necessary and sufficient conditions for geodesic curves and maps, and explored foliations and product manifolds.
result Necessary and sufficient conditions for various properties of Clairaut semi-invariant Riemannian maps were derived.
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.
Complete left-invariant metrics on Lie groups with specific properties.
problem Completeness of left-invariant semi-Riemannian metrics on Lie groups.
method Introducing bi-Lipschitz Riemannian Clairaut metrics and proving completeness conditions.
result All left-invariant metrics are complete for certain Lie groups.
We study the behavior of geodesics on a Randers surface of revolution. The main tool is the extension of Clairaut relation from Riemannian case to the Randers case. Moreover, we show that our Randers surface of revolution can be embedded in a Minkowski space as hypersurface.
Generalizes warped product submersion to conformal case.
problem Understanding angles preservation in submersions.
method Introduces conformal warped product submersion.
result Fundamental tensors derived for conformal submersion.
We introduce the notions of h-conformal slant submersions and almost h-conformal slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, slant submersions, h-slant submersions, almost h-slant submersion a…
Generalizes O'Neill's equations to pseudo-Finsler submersions.
problem Extending Riemannian submersion equations to pseudo-Finsler geometry.
method Generalization of O'Neill's fundamental equations to pseudo-Finsler submersions and exploration of O'Neill tensors.
result Generalized fundamental equations for pseudo-Finsler submersions.
As a generalization of Riemannian submersions, horizontally conformal submersions, semi-invariant submersions, h-semi-invariant submersions, almost h-semi-invariant submersions, conformal semi-invariant submersions, we introduce h-conformal semi-invariant submersions and almost h-conformal semi-invariant submersions fr…
We give a general Lie-theoretic construction for anti-invariant almost Hermitian Riemannian submersions, anti-invariant quaternion Riemannian submersions, anti-invariant para-Hermitian Riemannian submersions, anti-invariant para-quaternion Riemannian submersions, and anti-invariant octonian Riemannian submersions. This…
We study the geodesics on an invariant surface of a three dimensional Riemannian manifold. The main results are: the characterization of geodesic orbits; a Clairaut's relation and its geometric interpretation in some remarkable three dimensional spaces; the local description of the geodesics; the explicit description o…
The paper studies a new submersion type with specific conditions.
problem Characterizing a new submersion type in Riemannian geometry.
method Examining semi-invariant conformal ζ⊥-Riemannian submersions with horizontal Reeb vector field. result Conditions for the submersions to be totally geodesic and harmonic.
In this paper, we study biharmonic Riemannian submersions. We first derive bitension field of a general Riemannian submersion, we then use it to obtain biharmonic equations for Riemannian submersions with 1-dimensional fibers and Riemannian submersions with basic mean curvature vector fields of fibers. These are used…
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.
Study anti-invariant submersions from holomorphic statistical manifolds.
problem Understanding submersions in statistical manifolds.
method Introduced and analyzed anti-invariant holomorphic statistical submersions.
result Supported results with examples.
Akyol M.A. [Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistic, 46(2), (2017), 177-192.] defined and studied conformal anti-invariant submersions from cosymplectic manifolds. The aim of the present paper is to define and study the notion of conformal slant s…
As a generalization of semi-invariant submersions, we introduce conformal semi-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which are arisen from the definition of a conformal submersion and show that there are certain product …
Study on geometric properties of h-conformal semi-invariant submersions.
problem Exploring geometric characteristics of h-conformal semi-invariant submersions.
method Investigation of quaternionic Kähler manifolds and Riemannian manifolds, focusing on integrability of distributions and foliations.
result Established necessary and sufficient conditions for total geodesic submersions and twisted product manifolds.
Study of harmonic Riemannian submersions from 3D geometries.
problem Characterizing harmonic Riemannian submersions from specific 3D geometries.
method Using generalized integrability data and classifications of Thurston's 3D geometries, 3D BCV spaces, and Berger sphere.
result Complete classifications and explicit constructions of harmonic Riemannian submersions.
We introduce slant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions. We also find necessary and sufficient conditions for a slant s…
Akyol, M. A and Şahin, B. [Conformal semi-invariant submersions, Commun. Contemp. Math. 19, 1650011 (2017).] introduced the notion of conformal semi-invariant submersions from almost Hermitian manifolds. The present paper deal with the study of conformal generic submersions from almost Hermitian manifolds which extends…
Study of almost Yamabe solitons on Kaehler submersions.
problem Characterizing almost Yamabe solitons on Kaehler submersions.
method Analyzing conditions for solitons to be shrinking, steady, or expanding.
result Characterizations for almost Yamabe solitons in terms of extrinsic horizontal scalar curvature.
The paper classifies harmonic and biharmonic submersions from Sol space.
problem Classifying harmonic and biharmonic submersions from Sol space.
method Complete classification by proving non-existence and existence conditions.
result No harmonic or biharmonic submersion exists from Sol space to any surface.
In this paper, we study Riemannian submersions whose total manifolds admitting a Ricci soliton. Here, we characterize any fiber of such a submersion is Ricci soliton or almost Ricci soliton. Indeed, we obtain necessary conditions for which the target manifold of Riemannian submersion is a Ricci soliton. Moreover, we st…
We introduce anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian submersions defined on cosymplectic manifolds. We investigate necessary and sufficient condition for an anti-invariant Riemannian submersion to be totally geodesi…
We introduce slant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We survey main results of slant Riemannian submersions defined on Sasakian manifolds. We also give an example of such slant submersions.
The aim of the present paper to define and study semi-slant ξ⊥−Riemannian submersions from Sasakian manifolds onto Riemannian manifolds as a generalization of anti-invariant ξ⊥−Riemannian submersions, semi-invariant ξ⊥−Riemannian submersions and slant Riemannian submersions. We obtain characterizat…
Sharp inequalities and solitons studied in statistical submersions.
problem Understanding geometric properties of statistical submersions.
method Proving sharp inequalities and establishing geometrical properties of statistical submersions.
result Characterization of fibers as Ricci-Bourguignon solitons with conformal vector field.
The paper derives curvature inequalities for submersions from quaternionic space forms.
problem Deriving curvature inequalities for submersions from quaternionic space forms.
method Analyzing Ricci and scalar curvatures of horizontal and vertical distributions in anti-invariant submersions.
result Established Ricci curvature inequality for anti-invariant submersions.
We introduce bi-slant ξ⊥-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds as a generalization of slant and semi-slant ξ⊥-Riemannian submersion. We give an example and investigate the geometry foliations. After we obtain necessary and sufficient conditions related to totally geo…
Study cohomology classes related to harmonic maps on submersions.
problem Understanding harmonic maps on submersions and their cohomology.
method Extending previous results on Riemannian submersions and p-harmonic morphisms to F-harmonic and f-harmonic maps.
result Extend results on Riemannian submersions to F-harmonic and f-harmonic maps.
As a generalization of anti-invariant ξ⊥−Riemannian submersions, we introduce conformal anti-invariant ξ⊥−submersions from almost contact metric manifolds onto Riemannian manifolds. We investigate the geometry of foliations which are arisen from the definition of a conformal submersion and find necessary …