My research interests are in the area of Differential Geometry:
Einstein metrics, geometry of homogeneous metrics, symmetric
spaces, biquotients, equivariant geometry, and existence of closed
geodesics.
More recently, I have worked on the geometry and topology of
cohomogeneity one manifolds, and manifolds with non-negative or positive
sectional curvature.
Publications
-
M.Wang-W.Ziller,
On isotropy irreducible Riemannian manifolds,
Acta Math. 166 (1991), 223-261.
(
postscipt format ,
dvi format )
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D.DeTurck-W.Ziller,
Minimal isometric immersions of spherical space forms in spheres,
Comm. Math. Helv. 67 (1992), 428-458.
(
postscipt format ,
dvi format )
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M.Wang-W.Ziller,
Symmetric spaces and strongly isotropy irreducible spaces,
Math. Ann. 296 (1993), 285-326.
(
postscipt format ,
dvi format )
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E.Heintze-W.Ziller,
Isotropy irreducible spaces and s-representations,
Differential Geometry and its Applications 6 (1996) ,
181-188.
(
postscipt format ,
dvi format )
- W. Ziller,
Weakly symmetric spaces , in Topics in Geometry, Ed.
S.Gindinkin, Progress in Nonlinear Differential Equations, Vol. 20,
Birkhaeuser 1996, 355-368.
(
postscipt format ,
dvi format )
- G.Toth-W.Ziller,
Spherical minimal immersions of the 3-sphere,
Comm. Math. Helv. 74 (1999) , 1-34.
(
postscipt format ,
dvi format )
- K.Grove-W.Ziller, Curvature and Symmetry of Milnor Spheres,
Annals of Mathematics 152 (2000),331-367.
(
postscipt format ,
dvi format )
- K.Grove-W.Ziller, Cohomogeneity one manifolds with positive Ricci
curvature, Inv. Math. 149 ( 2002),619-649.
(
postscipt format ,
pdf format )
- V.Kapovitch-W.Ziller, Biquotients with singly generated rational
cohomology, Geom. Dedicata 104 (2004), 149-160 .
(postscript
format , pdf
format )
- C.Boehm-M.Wang-W.Ziller, A variational approach for compact
homogeneous Einstein manifolds, GAFA 14 (2004), 681-733.
(postscript
format , pdf
format )
- K.Grove-B.Wilking-L.Verdiani-W.Ziller, Non-negative curvature
obstruction in cohomogeneity one and the Kervaire spheres, Ann. del.
Scuola Norm. Sup. 5 (2006), 159-170.
(
pdf format
)
- K.Grove-K.Shankar-W.Ziller, Symmetries of Eschenburg spaces and the
Chern problem, Special Issue in honor of S.S.Chern, Asian J. Math. 10 (2006),
647-662.
(
pdf format
)
- T.Chinburg-C.Escher-W.Ziller, Topological properties of Eschenburg
spaces and 3-Sasakian manifolds, Math. Ann. 339 (2007), 3-20. (
pdf format ) A Maple file that computes the Kreck Stolz invariants of
an Eschenburg space using the formulas by Kruggel
Maple File
- L.Florit-W.Ziller, Orbifold fibrations of Eschenburg spaces, Geom. Ded. 127
(2007), 159-175.
(
pdf format )
- W.Ziller, Examples of Riemannian manifolds with non-negative sectional
curvature, in: Metric and Comparison Geometry, Surv. Diff. Gem. 11, ed. K.Grove and
J.Cheeger, International Press, 2007, p. 63-102.
(
pdf format )
- K.Grove-B.Wilking-W.Ziller, Positively curved cohomogeneity one
manifolds and 3-Sasakian geometry, J. Diff. Geom. 78 (2008), 33-111.
( pdf format )
- W.Ziller, Geometry of positively curved cohomogeneity one manifolds, in:
Riemannian
Topology and Geometric Structures on Manifolds, in honor of Charles Boyer's 65th
birthday, Progress in Mathematics, Birkhaeser, 2008.
(
pdf format )
- L.Florit-W.Ziller, On the topology of positively curved Bazaikin
spaces, J. Europ. Math. Soc. 11 (2009), 189-205.
(
pdf format
)
- L.Verdiania-W.Ziller, Positively curved homogeneous metrics on spheres, Math.
Zeitschrift 261 (2009), 473-488.
(
pdf format )
- K.Grove-W.Ziller, Lifting group actions and nonnegative curvature, Preprint
2008.( pdf
format
)
- K.Grove-L.Verdiani-W.Ziller, A new type of positively curved manifold, Preprint
2008. (pdf
format)
Maple file
Notes
-
A short summary of Eschenburg's Habilitation on biquotients which includes
a Table of his classification of biquotients of equal rank.
Eschenburg Summary
- A complete scanned version of Eschenburg's Habilitation.
Eschenburg Habilitation
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A short summary of Mueter's Ph.D. Thesis on Cheeger deformations.
Mueter Summary
- A complete scanned version of Mueter's Ph.D. thesis.
Mueter Thesis