Introduces conformal Riemannian morphisms generalizing various Riemannian concepts.
problem None explicitly stated; generalizing Riemannian concepts.
method Introduces conformal Riemannian morphisms and proves properties.
result Every injective conformal Riemannian morphism is an injective conformal immersion, and similar results for surjective and bijective cases.
Direct proof of cohomology isomorphism for pullback Lie algebroids.
problem Cohomology of pullback Lie algebroids under surjective submersions.
method Differential-geometric proof, leafwise cohomology vanishing, exhaustion-and-patching argument.
result Cohomology isomorphism and injectivity properties for pullback Lie algebroids.
Generalized Stacey-Roberts lemma for Banach manifolds.
problem Constructing Lie groupoids of smooth mappings in infinite-dimensional geometry.
method Generalization of the Stacey-Roberts lemma to Banach manifolds with smooth partitions of unity.
result Remedied an error in the original proof for finite-dimensional setting.
The procedure "Lie group --> Lie algebra" has a generalization "simplicial manifold --> L_infinity algebra", or yet better, "presheaf on the category of surjective submersions --> L_infinity algebra". We describe this generalization, together with its higher-order extensions.
Compact complex manifolds with trivial canonical bundle and ∂∂ˉ-Lemma have smooth deformations and a surjective Albanese map.
problem Understanding the structure and deformations of compact complex manifolds with specific properties.
method Analyzing the Kuranishi space, showing smooth deformations, and studying the Albanese map.
result Compact complex manifolds with trivial canonical bundle and ∂∂ˉ-Lemma have smooth deformations and a surjective Albanese map. This paper develops an algebraic structure for systems of systems and networks.
problem Formalizing interactions between complex systems and networks.
method Developing a monoidal double category of surjective submersions to encompass systems and maps between them.
result Recovering results on fibrations of networks of manifolds as a special case.
New proof of Lie algebroid action equivalence and integrability.
problem Equivalence between Lie algebroid action and integrability.
method Double Lie groupoids and multiplicative foliations.
result Simple characterization of double Lie groupoids inducing Lie groupoid structures.
We study isomorphism classes of symplectic dual pairs P <- S -> P-, where P is an integrable Poisson manifold, S is symplectic, and the two maps are complete, surjective Poisson submersions with connected and simply-connected fibres. For fixed P, these Morita self-equivalences of P form a group Pic(P) under a natural `…
Lie groupoids and their orbit spaces are linked through equivalence classes.
problem Understanding the relationship between Lie groupoids and their orbit spaces.
method Introducing lift-complete Lie groupoids and showing equivalence between categories.
result Morita equivalence class of a lift-complete Lie groupoid is determined by its orbit space.
Equivalent bicategories constructed from action Lie groupoids.
problem Equivalence of bicategories constructed from action Lie groupoids.
method Localizing at equivariant weak equivalences, surjective submersive equivariant weak equivalences, and all weak equivalences.
result Weak equivalences between action Lie groupoids are isomorphic to compositions of nice forms of equivariant weak equivalences.
Extends connections on Lie groupoids, proving completeness conditions.
problem Existence and completeness of multiplicative connections on Lie groupoid fibrations.
method Introduces and investigates multiplicative Ehresmann connections on Lie groupoid fibrations.
result Conditions for completeness of multiplicative connections on Lie groupoid fibrations.
In this article we prove first of all the nonexistence of holomorphic submersions other than covering maps between compact quotients of complex unit balls, with a proof that works equally well in a more general equivariant setting. For a non-equidimensional surjective holomorphic map between compact ball quotients, our…
New findings on how foliations and Lie group actions interact.
problem Understanding interactions between foliations and Lie group actions.
method Functorial properties of holonomy groupoids and quotient manifolds.
result Holonomy groupoids of quotients by Lie group actions exhibit similar properties.
Study on holomorphic isometries between complex domains, revealing geometric properties.
problem Characterizing holomorphic isometries between bounded symmetric domains.
method Analyzing holomorphic isometries between complex unit ball and other bounded symmetric domains, using classical results for complex-analytic subvarieties of Stein manifolds.
result Images of holomorphic isometries have specific geometric properties, including intersections with affine-linear subspaces.
In this paper, we undertake the study of the Tannaka duality construction for the ordinary representations of a proper Lie groupoid on vector bundles. We show that for each proper Lie groupoid G, the canonical homomorphism of G into the reconstructed groupoid T(G) is surjective, although, contrary to what happens in th…
Let X be a compact connected Kaehler manifold such that the holomorphic tangent bundle TX is numerically effective. A theorem of Demailly, Peternell and Schenider says that there is a finite unramified Galois covering M --> X, a complex torus T, and a holomorphic surjective submersion f: M --> T, such that the fibers o…
Introduces new types of submersions from quaternionic Hermitian manifolds.
problem Exploring new types of submersions in quaternionic geometry.
method Definition and investigation of h-conformal and almost h-conformal slant submersions.
result Properties and conditions for these submersions are studied.
Study new submersion types on quaternionic manifolds.
problem Explore new submersion types on quaternionic manifolds.
method Introduce and study h-conformal semi-invariant submersions and almost h-conformal semi-invariant submersions.
result Properties of these submersions, including foliations and geodesic conditions.
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.
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.
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.
The paper studies biharmonic submersions in Riemannian geometry.
problem Characterizing biharmonic Riemannian submersions.
method Deriving bitension field equations and using them to construct biharmonic examples and characterize submersions.
result Examples of proper biharmonic Riemannian submersions with 1-dimensional fibers and characterizations of warped products.
For a smooth (locally trivial) principal bundle in Ehresmann's sense, the relation between the commuting vertical and horizontal actions of the structural Lie group and the structural Lie groupoid (isomorphisms between vertical fibers) is regarded as a special case of a symmetrical concept of conjugation between "princ…
The paper defines and studies conformal slant submersions in contact geometry.
problem Understanding conformal slant submersions in contact geometry.
method Defining and studying conformal slant submersions from almost contact metric manifolds.
result Obtained geometries of the leaves of the distributions and conditions related to submersions.
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…
Bi-slant submersion generalizes slant and semi-slant submersion.
problem Generalizing submersion types in Riemannian geometry.
method Introducing and studying bi-slant ξ⊥-Riemannian submersions. result Necessary and sufficient conditions for totally geodesic submersion.
The paper studies conformal generic submersions from almost Hermitian manifolds.
problem Exploring new types of submersions in almost Hermitian manifolds.
method Extending existing submersions to study conformal generic submersions.
result Characterizations and properties of conformal generic submersions are obtained.
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.
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 characterizes submersions with Ricci soliton total manifolds and their properties.
problem Characterizing submersions with Ricci soliton total manifolds.
method Analyzing Riemannian submersions and their properties, focusing on fiber and target manifolds.
result Necessary conditions for the target manifold to be a Ricci soliton and characterizations of harmonicity.
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.
Abstract: Characterizations for submersions to be harmonic or biharmonic shown; examples provided.
problem Characterizing harmonic and biharmonic Riemannian submersions.
method Characterizations and examples provided.
result Characterizations and examples of submersions provided.
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.
Characterizes biharmonic constant mean curvature surfaces in Killing submersions.
problem Identifying biharmonic constant mean curvature surfaces in Killing submersions.
method Characterization through Riemannian submersions and unit Killing vector fields.
result Classification of proper biharmonic CMC surfaces and Hopf cylinders in Killing submersions.
A surjective submersion π:M→B carrying a field of simplectic structures on the fibres is symplectic if this Poisson structure is minimal. A symplectic submersion may be interpreted as a family of mechanical systems depending on a parameter in B. We give some conditions to find a closed form which represent the…
Study on a new type of submersion in geometry.
problem Exploring a new type of submersion in geometry.
method Introducing and investigating conformal anti-invariant ξ⊥−submersions. result Conditions for total geodesic and harmonic submersions.
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.
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.
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…
The paper defines and studies a new type of submersion from Sasakian manifolds.
problem Defining and studying a new type of submersion from Sasakian manifolds.
method Characterizations and geometry of foliations, necessary and sufficient conditions for specific properties.
result Characterizations and properties of the new submersion.
Study extends Riemannian submersion concepts to locally conformal Kaehler manifolds.
problem Extending Riemannian submersion concepts to new manifold types.
method Discussing geometry of foliations and obtaining decomposition theorems.
result Decomposition theorems for total manifolds of submersions.
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.
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.
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…
Real analytic submersion images are always real analytic.
problem Analyticity of submersion images
method Analyticity proof for Riemannian submersions
result Image of real analytic submersion is real analytic
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 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.