Advances in Differential Geometry and Curves
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "B: Geometry and Topology".
Deadline for manuscript submissions: 30 April 2027 | Viewed by 57
Editor
Interests: differential geometry (theory of curves and surfaces); Lorentz geometry; quaternion theory
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Differential geometry serves as the foundational language of the physical universe, evolving from classical local characterizations to the complex global analysis of modern manifolds. At the heart of this evolution lies the theory of curves and surfaces, which remains one of the most dynamic and vital areas of mathematical research.
This Special Issue aims to provide a high-impact platform for researchers to present original theorems, innovative derivations, and interdisciplinary applications. Our vision is to bridge the gap between classical geometric foundations and the computational demands of the 21st century.
We invite submissions that explore the intrinsic and extrinsic properties of geometric structures across various space forms, including Euclidean, Minkowski, and Galilean spaces. The scope of this issue includes, but is not limited to, the following core themes:
- Advanced Curve Theory:
The study of specialized curves provides essential insights into the topology and geometry of the spaces they inhabit. We are particularly interested in the following.
Specialized Characterizations: Research involving Salkowski curves, Smarandache curves, and the properties of pedal curves.
Frame Theory: Applications of the Frenet–Serret frame, Bishop frame, and alternative moving frames in characterizing curve behavior.
Geometric Invariants: New perspectives on curvature and torsion functions and their algebraic implications.
- Surfaces and Kinematic Geometry:
The transition from curves to surfaces represents a leap in structural complexity with direct applications in motion geometry and design.
Ruled and Translation Surfaces: Geometric analysis of ruled surfaces, their developability, and striction lines.
Bezier and Spline Surfaces: Computational and differential-geometric modeling of Bezier surfaces and their extensions.
Kinematics: The geometry of rigid body motions, axodes, and trajectory analysis within spatial kinematic systems.
- Singularity Theory and Geometric Flows:
Understanding the behavior of geometric structures at critical points and under continuous deformation is a frontier of modern geometry.
Singularity Analysis: Envelopes, focal surfaces, and the classification of singularities in smooth mappings.
Evolution Equations: The study of curve shortening flows and mean curvature flows in different manifold settings.
The beauty of differential geometry lies in its ability to combine aesthetic perfection with logical necessity. Your research in this field is vital to our collective understanding of geometric structures. I invite you to share your latest findings and contribute to a volume that will serve as a reference for years to come.
Dr. Süleyman Şenyurt
Guest Editor
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
Keywords
- differential geometry of curves and surfaces
- ruled surfaces and line geometry
- Lorentz–Minkowski geometry
- quaternionic and dual quaternionic curves
- kinematics and rigid body motions
- Bézier curves and surfaces
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