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The conformal geometry of surfaces recently developed by the authors leads to a unified understanding of algebraic curve theory and the geometry of surfaces on the basis of a quaternionic-valued function theory. The book offers an elementary introduction to the subject but takes the reader to rather advanced topics. Willmore surfaces in the foursphere, their Bäcklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.
All papers appearing in this volume are original research articles
and have not been published elsewhere. They meet the requirements
that are necessary for publication in a good quality primary
journal. E.Belchev, S.Hineva: On the minimal hypersurfaces of a
locally symmetric manifold. -N.Blasic, N.Bokan, P.Gilkey: The
spectral geometry of the Laplacian and the conformal Laplacian for
manifolds with boundary. -J.Bolton, W.M.Oxbury, L.Vrancken, L.M.
Woodward: Minimal immersions of RP2 into CPn. -W.Cieslak, A.
Miernowski, W.Mozgawa: Isoptics of a strictly convex curve.
-F.Dillen, L.Vrancken: Generalized Cayley surfaces. -A.Ferrandez,
O.J.Garay, P.Lucas: On a certain class of conformally flat
Euclidean hypersurfaces. -P.Gauduchon: Self-dual manifolds with
non-negative Ricci operator. -B.Hajduk: On the obstruction group
toexistence of Riemannian metrics of positive scalar curvature.
-U.Hammenstaedt: Compact manifolds with 1/4-pinched negative
curvature. -J.Jost, Xiaowei Peng: The geometry of moduli spaces of
stable vector bundles over Riemannian surfaces. - O.Kowalski,
F.Tricerri: A canonical connection for locally homogeneous
Riemannian manifolds. -M.Kozlowski: Some improper affine spheres in
A3. -R.Kusner: A maximum principle at infinity and the topology of
complete embedded surfaces with constant mean curvature. -Anmin Li:
Affine completeness and Euclidean completeness. -U.Lumiste: On
submanifolds with parallel higher order fundamental form in
Euclidean spaces. -A.Martinez, F.Milan: Convex affine surfaces with
constant affine mean curvature. -M.Min-Oo, E.A.Ruh, P.Tondeur:
Transversal curvature and tautness for Riemannian foliations.
-S.Montiel, A.Ros: Schroedinger operators associated to a
holomorphic map. -D.Motreanu: Generic existence of Morse functions
on infinite dimensional Riemannian manifolds and applications.
-B.Opozda: Some extensions of Radon's theorem.
All papers appearing in this volume are original research articles
and have not been published elsewhere. They meet the requirements
that are necessary for publication in a good quality primary
journal. E.Belchev, S.Hineva: On the minimal hypersurfaces of a
locally symmetric manifold. -N.Blasic, N.Bokan, P.Gilkey: The
spectral geometry of the Laplacian and the conformal Laplacian for
manifolds with boundary. -J.Bolton, W.M.Oxbury, L.Vrancken, L.M.
Woodward: Minimal immersions of RP2 into CPn. -W.Cieslak, A.
Miernowski, W.Mozgawa: Isoptics of a strictly convex curve.
-F.Dillen, L.Vrancken: Generalized Cayley surfaces. -A.Ferrandez,
O.J.Garay, P.Lucas: On a certain class of conformally flat
Euclidean hypersurfaces. -P.Gauduchon: Self-dual manifolds with
non-negative Ricci operator. -B.Hajduk: On the obstruction group
toexistence of Riemannian metrics of positive scalar curvature.
-U.Hammenstaedt: Compact manifolds with 1/4-pinched negative
curvature. -J.Jost, Xiaowei Peng: The geometry of moduli spaces of
stable vector bundles over Riemannian surfaces. - O.Kowalski,
F.Tricerri: A canonical connection for locally homogeneous
Riemannian manifolds. -M.Kozlowski: Some improper affine spheres in
A3. -R.Kusner: A maximum principle at infinity and the topology of
complete embedded surfaces with constant mean curvature. -Anmin Li:
Affine completeness and Euclidean completeness. -U.Lumiste: On
submanifolds with parallel higher order fundamental form in
Euclidean spaces. -A.Martinez, F.Milan: Convex affine surfaces with
constant affine mean curvature. -M.Min-Oo, E.A.Ruh, P.Tondeur:
Transversal curvature and tautness for Riemannian foliations.
-S.Montiel, A.Ros: Schroedinger operators associated to a
holomorphic map. -D.Motreanu: Generic existence of Morse functions
on infinite dimensional Riemannian manifolds and applications.
-B.Opozda: Some extensions of Radon's theorem.
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