Maximum curvature for curves in manifolds of sectional curvature at most zero or one

Strictly Kähler-Berwald manifolds with constant‎ ‎holomorphic sectional curvature

In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎. 

κ-Curves: Interpolation at Local Maximum Curvature

We present a method for constructing almost-everywhere curvature-continuous, piecewise-quadratic curves that interpolate a list of control points and have local maxima of curvature only at the control points. Our premise is that salient features of the curve should occur only at control points to avoid the creation of features unintended by the artist. While many artists prefer to use interpola...

On Stretch curvature of Finsler manifolds

In this paper, Finsler metrics with relatively non-negative (resp. non-positive), isotropic and constant stretch curvature are studied.  In particular, it is showed that every compact Finsler manifold with relatively non-positive (resp. non-negative) stretch curvature is a Landsberg metric. Also, it is proved that every  (α,β)-metric of non-zero constant flag curvature and non-zero relatively i...

Sectional Curvature in Piecewise Linear Manifolds

A metric complex M is a connected, locally-finite simplicial complex linearly embedded in some Euclidean space R. Metric complexes M and M' are isometric if they have subdivisions L and L and if there is a simplicial isomorphism h:L -• L such that for every a e L, the linear map determined by h\a -• h(a) is an isometry (that is, it extends to an isometry of the affine spaces generated by these ...

Curvature Estimates in Asymptotically At Manifolds of Positive Scalar Curvature