Dear Colleagues,

Special metrics arise naturally in Differential Geometry and Theoretical Physics. They are usually characterized by conditions on the curvature. The most important class of such metrics is the one of constant Ricci-curvature, or Einstein metrics. Such metrics are often the best candidates for the role of canonical metrics on manifolds and thus have a very important role in Topology. They have been also studied in theoretical physics, initially in General Relativity but more recently also in Superstring Theories.

One of the important objects associated with a metric is the holonomy group. The study of compact manifolds with special holonomy is relevant not only in Differential Geometry and Theoretical Physics, but also in relation with Algebraic Geometry.

The goal of this Special Issue is to provide a collection of research and survey papers that reflect the research on special (pseudo-)Riemannian metrics in Differential Geometry, in relation with Topology, Algebraic Geometry, and Superstring Theories.

We look forward to your contributions to this Special Issue,

Prof. Dr. Anna Maria Fino
Guest Editor

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• Einstein metric
• Ricci flat metric
• constant scalar curvature metrics
• holonomy group
• G₂
• Spin(7)
• Calabi–Yau manifold

• Applications of Differential Geometry in Axioms (9 articles)