Note on special curvature properties of m-th root metrics.
problem Characterizing m-th root metrics with specific curvature properties.
method Analyzing isotropic Landsberg curvature and almost vanishing H-curvature.
result m-th root metrics with isotropic Landsberg curvature reduce to Landsberg metrics.
In this paper, we define some non-Riemannian curvature properties for Cartan spaces. We consider Cartan space with the m-th root metric. We prove that every m-th root Cartan space of isotropic Landsberg curvature, or isotropic mean Landsberg curvature, or isotropic mean Berwald curvature reduces to a Landsberg, weakly …
In this note, adopting the pullback formalism of global Finsler geometry, we show by a counterexample that the kernel KerR of the h-curvature R of Cartan connection and the associated nullity distribution NR do not coincide, contrary to Akbar-Zadeh's result \cite{akbar.nul3.}. We give sufficient conditi…
The paper classifies and finds surfaces with specific curvature in isotropic spaces.
problem Finding surfaces with prescribed Gaussian and mean curvature in isotropic spaces.
method Classified and found surfaces of different types with specific curvature conditions.
result Affine factorable surfaces of different types with prescribed curvature were found and classified.
Two families of genus one surfaces with H-curvature in H2imesR are constructed.
problem Constructing surfaces with positive constant mean curvature in H2imesR. method Conjugate construction.
result There is no Schoen-type theorem for immersed surfaces with positive constant mean curvature in H2imesR. Study projective symmetries in Finsler spaces, showing reductions and constant flag curvature.
problem Exploring projective symmetries in Finsler spaces and their properties.
method Analyzing algebraic sub-algebras and curvature invariants of projective vector fields.
result Closed Finsler spaces with negative Ricci curvature reduce to Killing vector fields.
Study shows limits of volume-constrained sets are finite unions of Wulff shapes.
problem Analyzing the behavior of sets with degenerating ellipticity.
method Proving rigidity of L1-accumulation points of volume-constrained almost-critical sets. result Limits of volume-constrained sets are finite unions of φ-Wulff shapes. Study on generalized m-Kropina metrics in modified gravity and cosmology.
problem Understanding the geometric properties and applications of generalized m-Kropina metrics. method Proving the rationality of Finslerian geometric objects and studying the conditions for Einstein metrics.
result Conditions for a generalized m-Kropina metric to be an exact solution in modified gravity and cosmology. Investigates surfaces with prescribed mean and skew curvatures in Lorentz-Minkowski space.
problem Finding surfaces with prescribed mean and skew curvatures in Lorentz-Minkowski space.
method Rewriting the equations for mean and skew curvatures as linear first order ODEs with coefficients in hypercomplex numbers or real numbers.
result Solutions for surfaces of revolution with prescribed mean and skew curvatures.