Matches in SemOpenAlex for { <https://semopenalex.org/work/W156738339> ?p ?o ?g. }
Showing items 1 to 79 of
79
with 100 items per page.
- W156738339 endingPage "190" @default.
- W156738339 startingPage "143" @default.
- W156738339 abstract "This chapter is a study of isotropic and constant sectional curvature Finslerian manifolds. We first recall briefly the basics of Finslerian manifolds, define the isotropic manifolds and single out the properties of their curvature tensors. We then give a characterization of Finslerian manifolds with constant sectional curvature, generalizing Schur’s classical theorem. We next determine the necessary and sufficient conditions for an isotropic Finslerian manifold to be of constant sectional curvature. Our conditions bear on the Ricci directional curvature or on the second scalar curvature of Berwald. We show that the existence of normal geodesic coordinates of class C2 on isotropic manifolds forces them to be Riemannian or locally Minkowskian. We also deal with the case of compact isotropic Finslerian manifolds with strictly negative curvatures. In chapter III we give a classification of complete Finslerian manifolds with constant sectional curvatures. We prove that all geodesically complete Finslerian manifolds of dimension n > 2 with negative constant sectional curvature (K < 0) and with bounded torsion vector are Riemannian. We show that all simply connected Finslerian manifolds of dimension n > 2 with strictly positive constant sectional curvature and whose indicatrix is symmetric and has a scalar curvature independent of the direction is homeomorphic to an n-sphere. In the case when the Berwald curvature H vanishes and torsion tensor as well as its covariant vertical derivative are bounded we prove that the manifold in question is Minkowskian. In the last chapter we establish the ‘axioms of the plane’. By defining the totally geodesic, semi-parallel and auto-parallel Finslerian submanifolds we establish the criteria that permit to identify if a Finslerian manifold is of constant sectional curvature in the Berwald connection (axiom 1), in the Finslerian connection (axiom 2) or is Riemannian (axiom 3)." @default.
- W156738339 created "2016-06-24" @default.
- W156738339 creator A5030485736 @default.
- W156738339 date "2006-01-01" @default.
- W156738339 modified "2023-10-16" @default.
- W156738339 title "Finslerian Manifolds of Constant Sectional Curvature [4]" @default.
- W156738339 cites W2603651520 @default.
- W156738339 doi "https://doi.org/10.1016/s0924-6509(06)80008-5" @default.
- W156738339 hasPublicationYear "2006" @default.
- W156738339 type Work @default.
- W156738339 sameAs 156738339 @default.
- W156738339 citedByCount "0" @default.
- W156738339 crossrefType "book-chapter" @default.
- W156738339 hasAuthorship W156738339A5030485736 @default.
- W156738339 hasConcept C12089564 @default.
- W156738339 hasConcept C121332964 @default.
- W156738339 hasConcept C12520029 @default.
- W156738339 hasConcept C127413603 @default.
- W156738339 hasConcept C134306372 @default.
- W156738339 hasConcept C141071460 @default.
- W156738339 hasConcept C165818556 @default.
- W156738339 hasConcept C183517385 @default.
- W156738339 hasConcept C184050105 @default.
- W156738339 hasConcept C195065555 @default.
- W156738339 hasConcept C199360897 @default.
- W156738339 hasConcept C202444582 @default.
- W156738339 hasConcept C2524010 @default.
- W156738339 hasConcept C2777027219 @default.
- W156738339 hasConcept C2779668893 @default.
- W156738339 hasConcept C33923547 @default.
- W156738339 hasConcept C41008148 @default.
- W156738339 hasConcept C42448751 @default.
- W156738339 hasConcept C529865628 @default.
- W156738339 hasConcept C62520636 @default.
- W156738339 hasConcept C71924100 @default.
- W156738339 hasConcept C77461463 @default.
- W156738339 hasConcept C78519656 @default.
- W156738339 hasConceptScore W156738339C12089564 @default.
- W156738339 hasConceptScore W156738339C121332964 @default.
- W156738339 hasConceptScore W156738339C12520029 @default.
- W156738339 hasConceptScore W156738339C127413603 @default.
- W156738339 hasConceptScore W156738339C134306372 @default.
- W156738339 hasConceptScore W156738339C141071460 @default.
- W156738339 hasConceptScore W156738339C165818556 @default.
- W156738339 hasConceptScore W156738339C183517385 @default.
- W156738339 hasConceptScore W156738339C184050105 @default.
- W156738339 hasConceptScore W156738339C195065555 @default.
- W156738339 hasConceptScore W156738339C199360897 @default.
- W156738339 hasConceptScore W156738339C202444582 @default.
- W156738339 hasConceptScore W156738339C2524010 @default.
- W156738339 hasConceptScore W156738339C2777027219 @default.
- W156738339 hasConceptScore W156738339C2779668893 @default.
- W156738339 hasConceptScore W156738339C33923547 @default.
- W156738339 hasConceptScore W156738339C41008148 @default.
- W156738339 hasConceptScore W156738339C42448751 @default.
- W156738339 hasConceptScore W156738339C529865628 @default.
- W156738339 hasConceptScore W156738339C62520636 @default.
- W156738339 hasConceptScore W156738339C71924100 @default.
- W156738339 hasConceptScore W156738339C77461463 @default.
- W156738339 hasConceptScore W156738339C78519656 @default.
- W156738339 hasLocation W1567383391 @default.
- W156738339 hasOpenAccess W156738339 @default.
- W156738339 hasPrimaryLocation W1567383391 @default.
- W156738339 hasRelatedWork W2187554062 @default.
- W156738339 hasRelatedWork W2363787730 @default.
- W156738339 hasRelatedWork W2383363824 @default.
- W156738339 hasRelatedWork W2950778534 @default.
- W156738339 hasRelatedWork W2964060919 @default.
- W156738339 hasRelatedWork W3157473872 @default.
- W156738339 hasRelatedWork W3164452370 @default.
- W156738339 hasRelatedWork W3173707596 @default.
- W156738339 hasRelatedWork W3179425264 @default.
- W156738339 hasRelatedWork W4293156355 @default.
- W156738339 isParatext "false" @default.
- W156738339 isRetracted "false" @default.
- W156738339 magId "156738339" @default.
- W156738339 workType "book-chapter" @default.