 About 15,500 results  books.google.com 1568 Jacobi Zeta Function Jacobi's Imaginary Transformation Jacobi Zeta
Function Denoted zn(u.k) or Z(u). ... Jacobi's Curvature Theorem The principal
normal indicatrix of a closed SPACE CURVE with nonvanishing curvature bisects
the ... 

 books.google.com [I In Chapter 5 we will take up the question of finding conditions under which the
minimizing geodesic between two,points is unique. 4. The curvature tensor and
Jacobi fields From the Gauss Lemma we know that at veMp the deviation of (1 ... 

 books.google.com Proposition 12.1: Closed forms on contractible spaces Corollary 12.2: Poincare ́
lemma for closed forms Theorem 13.1: ... Theorem 16.6: Universal covers and
nonpositive sectional curvature Proposition 16.7: Characterization of Jacobi
fields ... 

 books.google.com G Gaussian curvature, 119 GaussOstrogradsky theorem, 71, 76 General
ellipsoid, 171 Generalized coordinates equation of virial oscillations, 120, 124–
132, 139 Jacobi function, 1,66–69 momentum, 76, 78, 262 virial theorem, 43,47,
50, 57, ... 

 books.google.com However, we did not estimate how large a region we could consider when we
studied how the curvature controlled the amount of distortion. In fact, the Jacobi
equation allows us to answer this question in many cases. 7.1 Ranch Theorem ... 

 books.google.com This text is designed for a onequarter or onesemester graduate course on Riemannian geometry. 

 books.google.com Proof. By definition, horizontal geodesics are contained in dual leaves. The
theorem follows once we show that the normal space to a leaf along some
geodesic contained in it is spanned by parallel Jacobi fields. Suppose then that
some dual ... 

 books.google.com Riemarmian manifolds of constant sectional curvature give most standard models
of Riemannian manifolds. In this chapter ... In §2, we state a comparison theorem
on Jacobi fields in a unified manner, and give some applications. In §§3 and 4 ... 

 books.google.com An Introduction to Curvature John M. Lee. C < 0, then no point of M has ... If C < 0,
the Jacobi field comparison theorem implies that any nontrivial normal Jacobi
field vanishing at t = 0 satisfies \J(t)\ > 0 for all t > 0. Similarly, if C > 0, then \J(t)\ ... 

 books.google.com 5.5 The Rauch Comparison Theorems and Other Jacobi Field Estimates We first
compare the three model spaces S", R", H" of curvature 1,0, –1. Let c(t) be a
geodesic with & = 1, we T.(0)M, Me {S", R", H"} with v = 1. The Jacobi field J(t) ... 

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