Geodesic
Generalized plane wave manifolds
Kragujevac Journal of Mathematics, Tome 28 (2005), p. 113 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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GENERALIZED PLANE WAVE MANIFOLDS Peter B. Gilkey1 and Stana Z. Nikcevic21Mathematics Department, University of Oregon,Eugene Or 97403 USA (email: gilkey@darkwing.uoregon.edu)2Mathematical Institute, SANU, Knez Mihailova 35, P. O. Box 367,11001 Belgrade, Serbia and Montenegro (email: stanan@mi.sanu.ac.yu) Abstract. We show that generalized plane wave manifolds are complete, strongly geodesically convex, Osserman, Szabó, and Ivanov-Petrova. We show their holonomy groups are nilpotent and that all the local Weyl scalar invariants of these manifolds vanish. We construct isometry invariants on certain families of these manifolds which are not of Weyl type. Given k, we exhibit manifolds of this type which are k-curvature homogeneous but not locally homogeneous. We also construct a manifold which is weakly 1-curvature homogeneous but not 1-curvature homogeneous.
Classification : 53C50 53C25 53B20
Keywords: affine curvature homogeneous, curvature homogeneous, geometry of the curvature tensor, holonomy, Ivanov-Petrova manifold, Osserman manifold, Szabo manifold, vanishing scalar curvature invariants, weakly curvature homogeneous, Weyl invariants 
@article{KJM_2005_28_a8,
     author = {Peter B. Gilkey and Stana \v{Z}. Nik\v{c}evi\'c},
     title = {Generalized plane wave manifolds},
     journal = {Kragujevac Journal of Mathematics},
     pages = {113 },
     year = {2005},
     volume = {28},
     zbl = {1143.53337},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2005_28_a8/}
}
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Peter B. Gilkey; Stana Ž. Nikčević. Generalized plane wave manifolds. Kragujevac Journal of Mathematics, Tome 28 (2005), p. 113 . http://geodesic.mathdoc.fr/item/KJM_2005_28_a8/