The study examines conditions for weak nearly cosymplectic manifolds to split into products.
problem Understanding the curvature and topology of weak nearly cosymplectic manifolds.
method Analyzes the conditions for splitting and characterizes specific manifolds.
result Conditions for weak nearly cosymplectic manifolds to become Riemannian products are identified.
Study weak f-K-contact manifolds, finding Einstein-type metrics and solitons.
problem Characterize and study geometric properties of weak f-K-contact manifolds. method Analyzing weak metric f-structures, using Killing vector fields, and Jacobi operators. result Einstein weak f-K-contact manifolds are Ricci flat. The study explores new metric structures on manifolds, linking them to Einstein metrics.
problem Characterizing and understanding weak K-contact manifolds and their properties.
method Analyzing weak K-contact manifolds and their properties, including the parallel Ricci tensor and generalized Ricci soliton structures.
result Sufficient conditions for weak K-contact manifolds with specific properties to be Einstein manifolds.
Study on Ricci solitons and Einstein metrics in weak β-Kenmotsu manifolds.
problem Characterizing Einstein metrics in weak β-Kenmotsu manifolds.
method Adapted ∗-Ricci tensor to weak almost contact manifolds and studied its interaction with weak β-Kenmotsu structures. result New characteristics of Einstein metrics obtained.
Defines weak geodesics on specific subsets of manifolds.
problem Characterizing geodesics on prox-regular subsets of Riemannian manifolds.
method Defining weak geodesics as continuous curves with weak regularities, and characterizing them as viscosity critical points of the energy functional.
result Characterizes weak geodesics on prox-regular subsets of Riemannian manifolds.
New structures defined for studying contact foliations and their geometry.
problem Understanding dynamics of contact foliations and their applications.
method Define and study weak nearly S- and weak nearly C-structures.
result Characterize weak nearly S- and weak nearly C- submanifolds in weak nearly Kähler manifolds.
Study weak quasi contact metric manifolds to generalize K-contact and Sasakian manifolds criteria.
problem Generalize K-contact and Sasakian manifolds criteria using weak quasi contact metric manifolds.
method Study weak quasi contact metric manifolds and generalize theorems for K-contact and Sasakian manifolds.
result Provide new criterions for K-contact and Sasakian manifolds in terms of curvature tensor and geometric objects.
Study on a new type of manifolds that generalize almost C-manifolds.
problem Understanding weak nearly C-manifolds and their properties.
method Analyzing conditions for local Riemannian product structures and characterizing specific dimensions.
result Conditions for a weak nearly C-manifold to become locally a Riemannian product and characterization of specific dimensions.
Optimizes shapes on non-standard manifolds.
problem Optimization on non-standard infinite-dimensional manifolds.
method Develops gradient descent on weak Riemannian manifolds.
result Establishes foundational properties for optimization on various weak Riemannian manifolds.
The paper characterizes Sasakian manifolds using weak nearly Sasakian structures.
problem Characterizing Sasakian manifolds using a new structure.
method Study of weak nearly Sasakian structures and proving theorems.
result Provides a new criterion for a weak almost contact metric manifold to be Sasakian.
Study ∗-η-Ricci solitons on weak Kenmotsu f-manifolds.
problem Characterize ∗-η-Ricci solitons on weak Kenmotsu f-manifolds. method Adapted ∗-Ricci tensor to weak metric f-manifolds, studied the interaction with weak βf-Kenmotsu structure. result Obtained new characteristics of η-Einstein metrics. The paper explores generalized Riemannian manifolds with weak metric structures.
problem Understanding weak metric structures on generalized Riemannian manifolds.
method Study of generalized metric connections, weak metric structures, and skew-symmetric torsion.
result Generalized Riemannian manifolds can be split into nearly Kähler manifolds.
The paper proves properties of curves in Riemannian manifolds.
problem Characterizing curves in Riemannian manifolds.
method Analyzing locally minimizing and weak geodesics.
result Locally minimizing curves are weak geodesics under certain conditions.
Compactifies Calabi-Yau to weak Fano manifolds.
problem Compactifying Calabi-Yau manifolds to weak Fano manifolds.
method Generalized Tian-Yau construction and asymptotically Calabi metrics.
result Calabi-Yau structure arises from compactification.
We study weakened f-structures on manifolds, generalizing classical results.
problem Classical f-structures and their properties on manifolds. method Introduced and studied weakened f-structures, subclasses, and their properties. result Generalized known results on globally framed f-manifolds. Introduces weak (p,k)-Dirac structures in geometric settings.
problem Defining and analyzing new geometric structures.
method Introducing and studying weak (p,k)-Dirac structures in TM⊕ΛpT∗M. result Weak (p,k)-Dirac structures contain more information than (p,k)-Lagrangian structures. Study of η-Ricci solitons and η-Einstein metrics on weak β-Kenmotsu f-manifolds.
problem Exploring new f-structures and their properties in geometric settings. method Analysis of weak β-Kenmotsu f-manifolds and their properties under η-Ricci soliton structures. result Weak β-Kenmotsu f-manifolds with β=const and η-Ricci soliton structures are η-Einstein manifolds of constant scalar curvature. The paper studies a new structure on contact manifolds and its foliation properties.
problem Investigating a new structure on contact manifolds.
method Examining weak nearly Sasakian structures and their foliations.
result The weak nearly Sasakian structure foliates into two types of totally geodesic foliations.
Unified proofs of weak holomorphic Morse inequalities using Bergman kernel functions.
problem Weak holomorphic Morse inequalities on various types of manifolds.
method Asymptotic Bergman kernel functions and Bochner-Kodaira-Nakano formulas.
result Unified proofs of weak holomorphic Morse inequalities.
Study on Kähler manifolds sharing submanifolds, proving projective implies relative.
problem Understanding Kähler manifolds sharing submanifolds.
method Proving properties of weak and strict relatives Kähler manifolds.
result If one Kähler manifold is projective and shares a submanifold with another, they are relatives.
Atiyah classes of DG manifolds of positive amplitude are invariant under weak equivalences.
problem Defining and studying Hochschild cohomology of DG manifolds of positive amplitude.
method Using poly-differential operators and derived intersection, proving invariance under weak equivalences.
result Hochschild cohomology of DG manifolds of positive amplitude is invariant under weak equivalences.
Survey on smooth function and form density in Riemannian Sobolev spaces.
problem Density of smooth functions and forms in Sobolev spaces on Riemannian manifolds.
method Careful examination of weak covariant derivatives and partial derivatives.
result Equivalence of weak covariant derivatives to weak partial derivatives.
Extends weak continuity of Yang-Mills connections to a broader class.
problem Weak compactness of Ω-Yang-Mills connections. method Compensation compactness argument applied to Yang-Mills fields.
result Weak continuity result extended to Ω-Yang-Mills connections. Survey of weak metric f-manifolds, generalizing K. Yano's structures.
problem Generalizing K. Yano's f-structures to new types of manifolds.
method Exploring new structures and properties of weak metric f-manifolds.
result New applications in geometry, including Killing vector fields and Ricci-type solitons.
Embeds flag manifolds into classical ones, proving rigidity in Kähler geometry.
problem Rigidity phenomena in homogeneous Kähler manifolds.
method Holomorphic isometric embeddings and rigidity analysis.
result No weak-relative relationship among flag manifolds, flat spaces, and homogeneous bounded domains.
We are concerned with the global weak rigidity of the Gauss-Codazzi-Ricci (GCR) equations on Riemannian manifolds and the corresponding isometric immersions of Riemannian manifolds into the Euclidean spaces. We develop a unified intrinsic approach to establish the global weak rigidity of both the GCR equations and isom…
This paper concerns the problem of integrability of non closed distributions on Banach manifolds. We introduce the notion of weak distribution and we look for conditions under which these distributions admit weak integral submanifolds. We give some applications to Banach Lie algebroid and Banach Lie-Poisson manifold. T…
Study curvature properties of w.a. S-manifolds with new conditions.
problem Curvature properties of weak almost S-manifolds.
method Partial Ricci flow, additional conditions, f-(κ,μ)-nullity.
result Characterize S-manifolds as limits of w.a. S-manifolds.
Survey of recent results in weak almost contact structures.
problem New geometric structures replacing complex structure in contact manifolds.
method Survey of recent findings in weak almost contact manifolds.
result Recent results on geodesic and Killing fields, rigidity and splitting theorems, etc.
We are concerned with the global weak continuity of the Cartan structural system -- or equivalently, the Gauss--Codazzi--Ricci system -- on semi-Riemannian manifolds with lower regularity. For this purpose, we first formulate and prove a geometric compensated compactness theorem on vector bundles over semi-Riemannian m…
Study on Kähler manifolds proves weak decompositions and relates harmonic forms.
problem Analyzing harmonic forms on Kähler manifolds.
method Proves weak W1,2 Bott-Chern and Dolbeault decompositions. result Strict relation between W1,2 Bott-Chern harmonic forms and the W1,2 Bott-Chern decomposition. This paper is devoted to give a complete unified study of several weak forms of $\ddb-$Lemma on compact complex manifolds.
New metric structures generalize Sasakian and cosymplectic structures, proving rigidity and finding conditions.
problem Generalizing Sasakian and cosymplectic structures to new metric structures.
method Introducing weak structures and proving rigidity of Sasakian structures.
result Any weak Sasakian structure is homothetically equivalent to a Sasakian structure.
Gradient estimates for solutions to a p-Laplacian equation on Riemannian manifolds.
problem Gradient estimates for positive weak solutions to a p-Laplacian equation on Riemannian manifolds.
method Morser iteration technique
result Gradient estimates show that positive weak solutions do not exist under certain conditions on manifolds with nonnegative Ricci curvature.
The paper studies symplectic forms on projective limits of Banach bundles and their Darboux Theorem.
problem Conditions for weak symplectic forms on projective limits of Banach bundles.
method Analyzing projective sequences of Banach bundles and applying Darboux Theorem.
result Necessary and sufficient conditions for the Darboux Theorem on projective limits of Banach manifolds.
Develops a diagrammatic method for symplectic filling classifications.
problem Classifying exact/weak symplectic fillings of 3D contact manifolds.
method Symplectic JSJ decomposition applied to contact surgery diagrams.
result Recover symplectic fillings for certain lens spaces and torus bundles, and classify fillings for a large class of plumbed 3-manifolds.
Study the geometry of weak para-f-structures and subclasses.
problem Understand the geometry of weak para-f-structures and their subclasses.
method Express covariant derivative of f, prove Killing characteristic vector fields, show foliations, and demonstrate rigidity.
result Prove that characteristic vector fields are Killing and ker f defines a totally geodesic foliation.
Preserves scalar curvature bounds under weak convergence of 3-manifolds.
problem Preserving scalar curvature bounds under weak convergence of 3-manifolds.
method Comparison between μ-bubbles in M_k and M.
result Scalar curvature lower bounds are preserved under weak convergence.
The paper explores new connections in non-symmetrical gravitational theory using weak metric structures.
problem Investigating linear connections in non-symmetrical gravitational models.
method Study of generalized Riemannian manifolds with weak metric structures and connections satisfying specific conditions.
result Proved properties of connections and structures in generalized Riemannian manifolds.
Study weak geodesic lines in Kähler metric space, disproving a conjecture.
problem Disproving a conjecture about weak geodesic lines in Kähler metrics.
method Establish Ross-Witt Nyström correspondence, construct weak geodesic lines.
result Some weak geodesic lines are smooth, disproving a popular conjecture.
In this paper we introduce a general notion of weak extension property for embeddings induced by a group actions. As an example, for the group H(M, m) of measure-preserving homeomorphisms of a noncompact manifold M, we deduce weak type extension theorems, and as an application we exhibit the local contractibility of th…
Develops L∞ spaces over dg manifolds and establishes an equivalence with L∞ algebroids.
problem Defining and comparing L∞ spaces and algebroids over dg manifolds. method Establishes an equivalence between categories of L∞ algebroids and L∞ spaces, constructs a faithful functor. result Detects weak equivalences between L∞ algebroids and L∞ spaces. New methods prove weak homotopy inequivalence for manifold symmetries.
problem Understanding symmetries of smooth 4-manifolds.
method Using Pin(-2)-monopole equations.
result New examples of 4-manifolds where symmetries are not fully represented.
We detail the construction of a weak Poisson bracket over a submanifold of a smooth manifold M with respect to a local foliation of this submanifold. Such a bracket satisfies a weak type Jacobi identity but may be viewed as a usual Poisson bracket on the space of leaves of the foliation. We then lift this weak Poisson …
We prove the Focal Index Lemma and the Rauch and Berger comparison theorems on a weak Riemannian Hilbert manifold with a smooth Levi-Civita connection and we apply these results to the free loop spaces of a compact manifold with the L^2 metrics
Proves curvature tensor convergence for smoothable spaces.
problem Curvature tensor behavior in smoothable Alexandrov spaces.
method Weak convergence of curvature tensors in noncollapsing sequences.
result Proves convergence of curvature tensors in smoothable Alexandrov spaces.
We study weak solutions to degenerate quasilinear elliptic equations, involving first order terms, in unbounded tubular domains. In particular we show that, under suitable hypotheses, the weak comparison principle holds if the domain is narrow enough.
We discuss the maximum modulus principle, and weak unique continuation, for CR functions on an abstract almost CR manifold M. We investigate these matters under the assumption of weak pseudoconcavity, and obtain sharp results about propagation along Sussmann leaves.