GEOMETRIAE DEDICATA
Scope & Guideline
Exploring the Depths of Geometric Science
Introduction
Aims and Scopes
- Differential Geometry and Riemannian Geometry:
The journal publishes articles exploring the properties and structures of differentiable manifolds, including studies of curvature, geodesics, and metrics, often employing Riemannian techniques. - Algebraic Geometry and Moduli Spaces:
Research on algebraic varieties, particularly moduli spaces, is a prominent theme, with a focus on their geometric structures and applications in other areas of mathematics. - Topology and Geometric Group Theory:
The journal covers topics in topology, including the study of manifolds, homotopy theory, and geometric group theory, emphasizing the interplay between algebraic and geometric methods. - Complex Geometry and Kähler Metrics:
Significant emphasis is placed on complex manifolds, Kähler metrics, and related structures, reflecting ongoing interests in both theoretical and applied aspects of complex geometry. - Dynamical Systems and Ergodic Theory:
Papers examining dynamical systems, particularly in geometric contexts, and their ergodic properties are also common, showcasing the journal's commitment to exploring motion and transformations within geometric frameworks.
Trending and Emerging
- Non-Positive Curvature and Metric Geometry:
A growing focus on non-positively curved spaces and their geometric properties is evident, highlighting their relevance in various mathematical contexts, including geometric group theory. - Geometric Group Theory:
The study of groups through geometric lenses is on the rise, with increased attention to their actions on spaces and implications for topological properties. - Interplay Between Geometry and Physics:
Research exploring the connections between geometric structures and physical theories, particularly in areas such as string theory and general relativity, is gaining traction, reflecting interdisciplinary interests. - Higher-Dimensional Geometry and Topological Methods:
There is an emerging trend towards higher-dimensional geometrical constructs and topological approaches, indicating a broadening of the journal's scope into more abstract settings. - Geometric Structures on Manifolds:
Papers examining various geometric structures on manifolds, including connections to algebraic topology and representation theory, are increasingly prevalent, showcasing the journal's commitment to contemporary issues in geometry.
Declining or Waning
- Classical Analysis in Geometry:
There has been a noticeable decline in papers focusing on classical analysis techniques applied to geometric problems, suggesting a shift towards more algebraic and topological methods. - Low-Dimensional Topology:
Research in low-dimensional topology, particularly studies related to 3-manifolds and knot theory, appears to be waning, with fewer submissions addressing these traditional topics. - Symplectic Geometry:
Symplectic geometry, once a vibrant area of interest, has seen fewer contributions, indicating a potential transition towards other geometric structures over the past few years.
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