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by M Brozos-Vázquez, P Gilkey, S Nikčević

Venue: | Nihonkai Math. J |

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by
Jianquan Ge, Zizhou Tang, Wenjiao Yan

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...erman conjectured that an Osserman manifold ( named later ) is a locally rank one symmetric space. This conjecture has been verified to be true except for the case when dimN=16 (cf. [Chi88], [Nik05], =-=[BGN09]-=-). In a locally rank one symmetric spaceNn+1 with non-constant sectional curvatures, all known examples of totally isoparametric hypersurfaces are homogeneous. Recall 8 J. Q. GE, Z. Z. TANG, AND W. J....

by
Y. Euh P. Gilkey

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...lishing geometric realization results, one often constructs examples which are only defined on a small neighborhood of 1 2 Y. EUH, P. GILKEY, J.H. PARK, AND K. SEKIGAWA the origin – the discussion in =-=[4]-=- provides a nice summary of these problems and we refer to other results in [5, 6, 15, 16]. And one wants to then deduce these geometric realization results also hold in the compact setting. 1.1. Tran...

by
P. Gilkey, S. Nikčević

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...U⋆± module, and that Λ2+ is not an irreducible U+ module. We complete our discussion of elementary representation theory with the following diagonalization result (see, for example, the discussion in =-=[7]-=-): Lemma 2.4. If ξ is a non-trivial proper U⋆± submodule of Λ2± ⊕ Λ2±, then there exists (a, b) 6= (0, 0) so ξ = ξ(a, b) := {(aθ, bθ)}θ∈Λ2± ⊂ Λ2± ⊕ Λ2±. 2.2. The Singer–Thorpe and the Higa decompositi...

by
Jianquan Ge
, 2011

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by
P. Gilkey, S. Nikčević

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... = S2±,J± ⊕ R⊕ S 2 0,∓,J± ⊕ Λ 2 ±,J± ⊕ χ⊕ Λ20,∓,J± . (2.a) The following decompositions were first established in [16, 22, 23] for almost complex structures in the positive definite case; we refer to =-=[5]-=- for the extension to the higher signature setting and to the almost para-complex case: Theorem 2.2. Adopt the notation established above. We have an orthogonal direct sum decompositions of non-trivia...

by
P. Gilkey, R. Vázquez-lorenzo

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...2] as is the complex setting [18, 19, 23]. The field is a vast one and we only cite a few representative recent examples. We introduce the following notational conventions and follow the treatment of =-=[2]-=- (Section 6.5) which is based on work of [6, 13, 28, 29]. Let R be the curvature operator of a Weyl connection ∇ and let R be the associated curvature tensor: R(x, y)z := (∇x∇y −∇y∇x −∇[x,y])z and R(x...

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