Cubics and negative curvature
نویسندگان
چکیده
منابع مشابه
Duality and Riemannian cubics
Riemannian cubics are curves used for interpolation in Riemannian manifolds. Applications in trajectory planning for rigid bodiy motion emphasise the group SO(3) of rotations of Euclidean 3-space. It is known that a Riemannian cubic in a Lie group G with bi-invariant Riemannian metric defines a Lie quadratic V in the Lie algebra, and satisfies a linking equation. Results of the present paper in...
متن کاملMannifolds of Negative Curvature
A C∞ function f on a riemannian manifold M is convex provided its hessian (second covariant differential) is positive semidefinite, or equivalently if (f ◦σ)′′ ≥ 0 for every geodesic inM . We shall apply this notion in a variety of ways to the study of manifolds of negative or nonpositive curvature. Convexity has, of course, long been associated with negative curvature, but convex function seem...
متن کاملCollineations, Conjugacies, and Cubics
If F is an involution and φ a suitable collineation, then φ ◦ F ◦ φ−1 is an involution; this form includes well-known conjugacies and new conjugacies, including aleph, beth, complementary, and anticomplementary. If Z(U) is the self-isogonal cubic with pivot U , then φ carries Z(U) to a pivotal cubic. Particular attention is given to the Darboux and Lucas cubics, D and L, and conjugacy-preservin...
متن کاملRamanujan-nagell Cubics
A well-known result of Beukers [3] on the generalized Ramanujan-Nagell equation has, at its heart, a lower bound on the quantity |x2 − 2n|. In this paper, we derive an inequality of the shape |x3 − 2n| ≥ x4/3, valid provided x3 6= 2n and (x, n) 6= (5, 7), and then discuss its implications for a variety of Diophantine problems.
متن کاملRigidity in Non-negative Curvature
In this paper we will show that any complete manifold of nonnegative curvature has a flat soul provided it has curvature going to zero at infinity. We also show some similar results about manifolds with bounded curvature at infinity. To establish these theorems we will prove some rigidity results for Riemannian submersions, eg., any Riemannian submersion with complete flat total space and compa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2012
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2012.09.004