Explicit Formulas for the Geodesics of Homogeneous SO(2)-Isotropic Three-Dimensional Manifolds
نویسندگان
چکیده
منابع مشابه
Three Dimensional Manifolds All of Whose Geodesics Are Closed
Three Dimensional Manifolds All of Whose Geodesics Are Closed John Olsen Wolfgang Ziller, Advisor We present some results concerning the Morse Theory of the energy function on the free loop space of S for metrics all of whose geodesics are closed. We also show how these results may be regarded as partial results on the Berger Conjecture in dimension three.
متن کاملNull Geodesics in Five-Dimensional Manifolds
We analyze a class of 5D non-compact warped-product spaces characterized by metrics that depend on the extra coordinate via a conformal factor. Our model is closely related to the so-called canonical coordinate gauge of Mashhoon et al. We confirm that if the 5D manifold in our model is Ricciflat, then there is an induced cosmological constant in the 4D sub-manifold. We derive the general form o...
متن کاملLow-dimensional Homogeneous Einstein Manifolds
A closed Riemannian manifold (Mn, g) is called Einstein if the Ricci tensor of g is a multiple of itself; that is, ric(g) = λ · g. This equation, called the Einstein equation, is a complicated system of second order partial differential equations, and at the present time no general existence results for Einstein metrics are known. However, there are results for many interesting classes of Einst...
متن کاملHomogeneous Geodesics of Left Invariant Randers Metrics on a Three-Dimensional Lie Group
In this paper we study homogeneous geodesics in a three-dimensional connected Lie group G equipped with a left invariant Randers metric and investigates the set of all homogeneous geodesics. We show that there is a three-dimensional unimodular Lie group with a left invariant non-Berwaldian Randers metric which admits exactly one homogeneous geodesic through the identity element. Mathematics Sub...
متن کاملExplicit Concave Fillings of Contact Three-manifolds
When (M, ξ) is a contact 3-manifold we say that a compact symplectic 4-manifold (X,ω) is a concave filling of (M, ξ) ifM = −∂X and if there exists a Liouville vector field V defined on a neighborhood of M , transverse to M and pointing in to X , such that ξ is the kernel of ıV ω restricted toM . We give explicit, handleby-handle constructions of concave fillings of all closed, oriented, contact...
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: Advances in Mathematics
سال: 2000
ISSN: 0001-8708
DOI: 10.1006/aima.2000.1950