### Table 2: Riemannian A-manifolds Parallel forms

"... In PAGE 11: ... Complete examples of (special) O-manifolds are constructed by Bryant and Salamon [6] and compact examples are constructed by Joyce [14], and recently by Kovalev [17]. In Table2 , we list the various parallel forms on A-manifolds, in the Euclidean case.2 Remark.... ..."

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### Table 1: Re-interpretation of addition and subtraction in a Riemannian manifold.

2006

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### Table 1: Re-interpretation of addition and subtraction in a Riemannian manifold.

2006

Cited by 28

### Table 1. Riemannian symmetric pairs with even multiplicities.

"... In PAGE 23: ... The list has been extracted from the classi cation due to Oshima and Sekiguchi [OS80]. It is presented in three tables respectively collecting (for the even multiplicity case) the Riemannian symmetric pairs ( Table1 ), the non-compactly causal (NCC) symmetric pairs (Table 2) and the other K quot; symmetric pairs (Table 3). A non-Riemannian K quot;-symmetric pair is said to be of type K quot;I if its signature quot; comes from a gradation of rst kind according to [Ka96].... ..."

### Table 5 summarizes 1 2A-Lagrangian submanifolds in Riemannian A- manifolds and their common names.

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### Table 3.14 - Weakly symmetric homogeneous manifolds of a connected compact simple Lie group M = G=H weakly symmetric with respect to

"... In PAGE 3: ... We note that the homogeneous manifold SO(8)=(SU(2) Sp(2)) appearing on Kramer apos;s list is also a symmetric space (cf. [WZ], Table3 , p. 325).... ..."

### Table 2. Model Curv. Geo. Exceptional Set Function

1998

"... In PAGE 32: ...e nition 5.7. Let N be a manifold and : N ! R be a function. Then B N has the compact intersection property with respect to if for every compact interval [a; b] R the set fx 2 B : (x) 2 [a; b]g has compact closure in N. The rigidity results of this section are of the following type: Let k = 0 or k = 1 and let (Rn k(K0); gRn k(K0)) be a model space (by which we mean one of the spaces listed in Table2 ) and (M; g) a semi-Riemannian manifold of the same dimension and index as Rn k(K0). Let B Rn k(K0) be a closed set and f : (Rn k(K0)nB) ! M a local isometry.... In PAGE 32: ... The basic conditions are that B not be too large (which will usually mean that it have the compact intersection property with respect to some function ), that Rn k(K0) n B be connected (which is easily seen to be necessary) and that (M; g) is geodesically complete with respect to geodesics of some sign. Table2 summarizes the conditions on the model space, the curvature bounds, the sign of the complete geodesics (column headed... In PAGE 33: ...8. Let (Rn k(K0); gRn k(K0)) be one of the model spaces in Table2 of dimension at least three and let B Rn k(K0) be a closed set so that Rn... ..."

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### Table 2 of dimension at least three and let B Rn k(K0) be a closed set

1998

"... In PAGE 32: ...e nition 5.7. Let N be a manifold and : N ! R be a function. Then B N has the compact intersection property with respect to if for every compact interval [a; b] R the set fx 2 B : (x) 2 [a; b]g has compact closure in N. The rigidity results of this section are of the following type: Let k = 0 or k = 1 and let (Rn k(K0); gRn k(K0)) be a model space (by which we mean one of the spaces listed in Table2 ) and (M; g) a semi-Riemannian manifold of the same dimension and index as Rn k(K0). Let B Rn k(K0) be a closed set and f : (Rn k(K0)nB) ! M a local isometry.... In PAGE 32: ... The basic conditions are that B not be too large (which will usually mean that it have the compact intersection property with respect to some function ), that Rn k(K0) n B be connected (which is easily seen to be necessary) and that (M; g) is geodesically complete with respect to geodesics of some sign. Table2 summarizes the conditions on the model space, the curvature bounds, the sign of the complete geodesics (column headed... ..."

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### Table 1: Manifold Variables Manifold M T @

1995

"... In PAGE 6: ... For such an observer, the velocity is just the normal vector u , and the acceleration of the normal vector is given by a = u r u = N?1h r N. A summary of the notation described above is given in Table1 of the ap- pendix. 2.... In PAGE 38: ... Foliation of M along I allows us to de ne the lapse, N, and the shift, N . The various manifolds we will consider, and some of the tensors de ned on them are summarized in Table1 . We can construct the following densities on Table 1: Manifold Variables Manifold M T @ ... ..."

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### Table 3 The tables show that hyperbolic 2- or 3-manifolds of nite volume with one end behave like compact ones, the Dirac spectrum is always discrete. A surface with two or more ends always admits both types of spin structures. This is not true for 3-manifolds. Discrete spectrum is always possible but the case spec(D) = R only sometimes. If the hyperbolic 3-manifold is topologically given as the complement of a link in S3 (and this construction is one of the main sources for hyperbolic 3-manifolds of nite volume), then this question can be decided. Theorem 9.2 (Bar [7]). | Let K S3 be a link, let M = S3?K carry a hyperbolic metric of nite volume.

2000

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