The paper proves a Schwarz lemma for weakly Kähler-Finsler manifolds.
problem Estimating distance functions and proving Schwarz lemma for weakly Kähler-Finsler manifolds.
method Establishing theorems about distance functions and applying them to prove the Schwarz lemma.
result Holomorphic mappings from weakly Kähler-Finsler manifolds to pseudoconvex Finsler manifolds are constant under certain conditions.
The paper studies complex Finsler metrics and curvature inequalities.
problem Analyzing holomorphic sectional curvature in complex Finsler manifolds.
method Developed an inequality relating holomorphic sectional curvature and proved Schwarz Lemma.
result Complex Finsler manifolds with semi-positive but not identically zero holomorphic sectional curvature have negative Kodaira dimension under certain conditions.
The paper extends Montel's theorem to complex Finsler manifolds.
problem Understanding normal families of holomorphic mappings in complex Finsler geometry.
method Proves a theorem for normal families of holomorphic mappings between complex Finsler manifolds.
result Extends Montel's theorem to complex Finsler manifolds.
It is proved that all invariant functions of a complex Finsler manifold can be totally recovered from the torsion and curvature of the connection introduced by Kobayashi for holomorphic vector bundles with complex Finsler structures. Equations of the geodesics and Jacobi fields of a generic complex Finsler manifold, ex…
In this paper, we investigate the two-dimensional complex Finsler manifolds. The tools of this study are the complex Berwald frames and the Chern-Finsler connection with respect to these frames.
Study curvature of complex Finsler metrics on Lie groups.
problem Explicitly calculate and characterize curvature of complex Finsler metrics.
method Analyzes left-invariant complex Finsler metrics on Lie groups using their Lie algebra.
result Characterizes conditions for a Finsler metric to be Kähler or weakly Kähler.
Characterizes complex Finsler metrics and their properties.
problem Characterize complex Finsler metrics and their geometric properties.
method Defined the canonical connection and investigated holomorphic sectional curvature tensors and Ricci curvatures.
result Characterizes balanced complex Finsler metrics and provides sufficient and necessary conditions.
In this paper, we establish a Gauss-Bonnet-Chern theorem for general closed complex Finsler manifolds.
Study on Kähler Finsler manifolds with curvature bounds, proving theorems.
problem Understanding Kähler Finsler manifolds with curvature constraints.
method Analyzing partial parallelism of complex structure, proving theorems.
result Generalized comparison theorem for positively curved Kähler Finsler manifolds.
Proves complex Finsler bundles with positive curvature are ample and biholomorphic to projective space.
problem Solving a 1975 problem posed by S. Kobayashi about complex Finsler vector bundles with positive Kobayashi curvature.
method Analyzes properties of complex Finsler vector bundles with positive Kobayashi curvature.
result Complex Finsler vector bundles with positive Kobayashi curvature are ample and biholomorphic to projective space.
The paper proves a Schwarz lemma for mappings between specific types of manifolds.
problem Establishing a Schwarz lemma for mappings between Kähler and complex Finsler manifolds.
method Using properties of holomorphic sectional curvature and radial sectional curvature.
result A Schwarz lemma for holomorphic mappings between Kähler and complex Finsler manifolds.
Study on conformal deformations of complex Finsler metrics.
problem Characterization and stability of Kähler Finsler metrics.
method Characterization and study of critical points in conformal classes.
result Stability of critical Kähler Finsler metrics obtained.
The paper studies complex Finsler metrics and their equivalence to the Kobayashi metric.
problem Investigating properties and equivalence of complex Finsler metrics.
method Using curvature properties of Bergman metrics and Schwarz lemma, the paper analyzes complex Finsler metrics and their equivalence to the Kobayashi metric.
result Uniform equivalences of the Kobayashi metric and Carathéodory metric on bounded strongly convex domains with smooth boundaries are proven.
For a strongly pseudo-convex complex Finsler manifold M, a bundle U of adapted unitary frames is canonically defined. A non-linear Hermitian connection on U, invariant under local biholomorphic isometries, is given and it proved to be unique. By means of such connection, an absolute parallelism on U is determined and a…
Characterizes Kähler-Berwald metrics on complex manifolds.
problem Identifying Kähler-Berwald metrics among strongly convex complex Finsler metrics.
method Geometric characterization using Cartan and Chern-Finsler connections.
result Characterizes Kähler-Berwald metrics in terms of parallelism of the canonical complex structure.
The paper characterizes complex Finsler metrics invariant under U(n) and their properties.
problem Characterizing U(n)-invariant strongly convex complex Finsler metrics. method Analyzing conditions for strong convexity and proving theorems about these metrics.
result A U(n)-invariant strongly convex complex Finsler metric is a real Berwald metric if and only if it comes from a Hermitian metric. In this paper, we introduce horizontal and vertical warped product Finsler manifold. We prove that every C-reducible or proper Berwaldian doubly warped product Finsler manifold is Riemannian. Then, we find the relation between Riemmanian curvatures of doubly warped product Finsler manifold and its components, and consi…
Paper finds conditions for two geodesics on complex manifolds.
problem Existence of two distinct closed geodesics on manifolds with infinite fundamental group.
method Topological and metric conditions for existence of geodesics in Riemannian and Finsler metrics.
result Generic Finsler metrics have two distinct closed geodesics.
In this paper, we solve a problem of Kobayashi posed in \cite{Ko4} by introducing a Donaldson type functional on the space F+(E) of strongly pseudo-convex complex Finsler metrics on E -- a holomorphic vector bundle over a closed Kähler manifold M. This Donaldson type functional is a generalization in the complex…
The paper studies metrics on hyperkähler manifolds using sub-twistor constraints.
problem Understanding metrics on hyperkähler manifolds with non-holonomic constraints.
method Introducing and analyzing sub-conic metrics, showing they are sub-Finsler.
result Explicit description of Finsler norms for sub-twistor metrics.
Smooth Busemann functions found in harmonic Finsler spaces.
problem Analyzing Busemann functions in Finsler manifolds.
method Investigation of Busemann functions in general and asymptotically harmonic Finsler manifolds.
result Smoothness of Busemann functions on asymptotically harmonic Finsler manifolds.
The study introduces new tensors for almost Finsler manifolds and analyzes their properties.
problem Defining and analyzing new types of Finsler manifolds.
method Introducing new Finsler manifolds, studying their properties, and deriving characteristic tensors.
result Characteristic tensors for almost Finsler manifolds have been generalized and their properties have been studied.
Paper solves open problem in complex Finsler geometry.
problem Existence of non-Kähler weakly Kähler Finsler metrics.
method Constructs a family of weakly Kähler Finsler metrics.
result Proves uniformization theorem for unitary invariant complex Randers metrics.
The paper derives inequalities on Finsler manifolds, influenced by their curvatures.
problem Deriving inequalities on Finsler manifolds.
method Local and global geometric inequalities on Riemannian and Finsler manifolds.
result Generalized Caffarelli-Kohn-Nirenberg and Hardy type inequalities on Finsler manifolds.
Introduces singular Finsler foliations and their properties.
problem Generalizing Finsler actions, submersions, and foliations.
method Definition and analysis of singular Finsler foliations on Randers manifolds.
result Singular Finsler foliations on Randers manifolds are singular Riemannian foliations on the Riemannian manifold induced by the metric.
The paper explores harmonic and asymptotically harmonic Finsler manifolds and their properties.
problem Characterizing and understanding harmonic Finsler manifolds.
method Investigation of various types of harmonic Finsler manifolds, characterizations via mean curvature and Laplacian, and construction techniques.
result Certain harmonic Finsler manifolds are of Einstein type and examples of non-Riemannian Finsler harmonic manifolds are provided.
The paper proves short-time existence and uniqueness of Ricci flow on Finsler manifolds.
problem Existence and uniqueness of Ricci flow solutions on Finsler manifolds.
method Investigation of short-time existence and uniqueness of Ricci flow solutions on Finsler manifolds.
result Theorems demonstrating the short-time existence of the flow solution for n-dimensional Finsler manifolds and the uniqueness of the solution for isotropic Finsler manifolds.
No non-trivial convex functions on certain Finsler manifolds.
problem Existence of convex functions on Finsler manifolds.
method Analyzing Holmes- Thompson volume and Busemann function properties.
result Non-compact Finsler manifolds with infinite Holmes- Thompson volume have no non-trivial convex functions.
The paper proves a theorem about Finsler manifolds and their diameters.
problem Understanding the maximum diameter of Finsler manifolds.
method Analyzing weighted Ricci curvature and applying it to the diameter.
result Finsler manifolds with maximal diameter are isometric to standard Finsler spheres.
The paper characterizes complex Finsler metrics that are projectively flat or dually flat.
problem Characterizing complex Finsler metrics with specific geometric properties.
method Proving conditions for projective flatness and dually flatness in terms of Minkowski metrics.
result Strongly convex complex Finsler metrics are projectively flat or dually flat if and only if they come from Minkowski metrics.
New TDA approach using Finsler metrics.
problem Traditional TDA concepts and methods.
method Introducing Finsler metrics for TDA.
result Relevance of Finsler metrics to TDA.
The study examines Einstein-Finsler spaces using Minkowskian products.
problem Characterizing Einstein-Finsler spaces through Minkowskian products.
method Proving conditions for Einstein-Finsler spaces in terms of Minkowskian products.
result If a Minkowskian product Finsler manifold is Einstein, then either the product manifold is Ricci flat or both quotient manifolds are Einstein with same scalar functions.
The paper calculates curvature formulas for stable Higgs bundles.
problem Investigating the geometry of stable Higgs bundles over complex manifolds.
method Applying curvature formulas from Schumacher-Toma and Biswas-Schumacher to calculate and analyze the curvature of the base manifold.
result Explicit calculation of holomorphic sectional curvature for a complex Finsler metric.
The paper studies Finsler manifolds and their integral curvatures.
problem Understanding the curvature of Finsler manifolds.
method Proves Myers type theorems on integral curvatures of Finsler manifolds.
result Establishes diameter estimates based on integral curvature bounds.
We generalize and study the Zermelo navigation problem on Hermitian manifolds in the presence of a perturbation W determined by a mild complex velocity vector field ∣∣W(z)∣∣h<∣∣u(z)∣∣h, with application of complex Finsler metric of complex Randers type. By admitting space-dependence of ship's relative speed $||u(…
Defines a new type of Finsler space with specific metrics.
problem Defines a new type of Finsler space with specific metrics.
method Defines and studies a new type of Finsler space with Infinite Series (α,β)-metric. result Properties of the new Finsler space are studied.
Based on a self-contained, coordinate-free exposition of the necessary concepts and tools of spray and Finsler geometry (with detailed proofs), we derive new results among others on the consequences of the direction-independence of the Landsberg tensor and the stretch tensor of a Finsler manifold. We show that an at le…
The paper defines semi-concurrent vector fields on Finsler manifolds and explores their implications.
problem Characterizing Finsler manifolds with semi-concurrent vector fields.
method Introducing and investigating semi-concurrent vector fields, proving properties, and providing examples.
result Finsler manifolds admitting semi-concurrent vector fields are either Riemannian or conic Finslerian.
The study establishes inequalities on Finsler manifolds with weighted Ricci curvature.
problem Investigating inequalities on Finsler manifolds with weighted Ricci curvature.
method Volume comparison, Bonnet-Myers theorem, Poincaré-Lichnerowicz inequality.
result Sharp lower bound for the first eigenvalue on Finsler manifolds.
The paper discusses fundamental problems in global Finsler geometry.
problem Fundamental problems in global Finsler geometry.
method Optimization and improvement of Lie derivatives, characterization of gradient vector fields, gradient estimate.
result Gradient estimate for smooth functions on Randers manifolds.
The study extends Obata's theorem and classifies Finsler manifolds with transnormal functions.
problem Classifying Finsler manifolds based on geometric properties.
method Extending Obata's theorem and using a second order differential equation.
result Complete Finsler manifolds of positive constant flag curvature are homeomorphic to spheres.
Paper sharpens Hardy and Rellich inequalities on nonreversible Finsler manifolds.
problem Quantitative Hardy and Rellich inequalities on nonreversible Finsler manifolds.
method Sharp constants of inequalities refined with remainder terms for specific curvature conditions.
result Results hold globally for nonreversible Finsler manifolds with certain curvature properties.
This article is an exposition of four loosely related remarks on the geometry of Finsler manifolds with constant positive flag curvature. <p> The first remark is that there is a canonical Kahler structure on the space of geodesics of such a manifold. <p> The second remark is that there is a natural way to construct a (…
On the product of two Finsler manifolds M1 M2, we consider the twisted metric F which is construct by using Finsler metrics F1 and F2 on the manifolds M1 and M2, respectively. We introduce horizontal and vertical distributions on twisted product Finsler manifold and study Creducible and semi-C-reducible properties of t…
The paper explores properties of Finsler manifolds with specific curvature conditions.
problem Investigating Finsler metrics with various curvature conditions.
method Analyzing non-Riemannian (α,β)-metrics and compact Finsler manifolds with specific curvature properties. result Compact Finsler manifolds with relatively non-negative stretch curvature are Landsberg metrics.
Paper proves at least two closed geodesics on compact Finsler manifolds.
problem Existence of closed geodesics on compact Finsler manifolds.
method Analyzes compact bumpy Finsler manifolds with finite fundamental group.
result Proves at least two closed geodesics on compact Finsler manifolds.
Most Finsler metrics have infinite-dimensional holonomy groups.
problem Understanding the holonomy groups of Finsler metrics.
method Analyzing the set of Finsler metrics on a manifold.
result An open dense subset of Finsler metrics have infinite-dimensional holonomy groups.
The paper derives Harnack inequalities for positive heat equation solutions on Finsler manifolds.
problem Deriving inequalities for heat equation solutions on Finsler manifolds.
method Generalizing Li-Yau type gradient estimates to Finsler geometry and applying to heat equation solutions.
result General gradient estimate for positive solutions of the heat equation on Finsler manifolds under curvature assumptions.