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Topological Properties of Magnetic and Vorticity Fields
The interior media of stars and planets are often virtually perfect conductors and possess magnetic fields. These fields are said to be “frozen" into...
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Cotton tensor, Bach tensor and Kenmotsu manifolds
It is known that Einstein metrics are Bach flat . So, the question may arises whether there exists any Riemannian metric which is Bach flat but not...
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Projective and Affine Quadrics
Dupin ring cyclide with a three-web consisting of Villarceau circles of both kinds and of isogonal trajectories of the circular curvature lines. In a...
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Conjugate Plateau Constructions in Product Spaces
This survey paper investigates, from a purely geometric point of view, Daniel’s isometric conjugation between minimal and constant mean curvature...
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Pieri’s Works on Foundations and Philosophy of Mathematics
This chapter discusses Pieri’s individual published works on foundations and philosophy of mathematics, as well as his unpublished but surviving...
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Kinematic Fast Dynamo Problems
Stars and planets possess magnetic fields that permanently change. Earth, for instance, mysteriously interchanges its north and south magnetic poles,...
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Traveling Wave Solutions of the Kawahara Equation Joining Distinct Periodic Waves
The Kawahara equation is a weakly nonlinear longwave model of dispersive waves that emerges when leading, third order, dispersive effects are in...
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Information geometry of dynamics on graphs and hypergraphs
We introduce a new information-geometric structure associated with the dynamics on discrete objects such as graphs and hypergraphs. The presented...
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Vector-relation configurations and plabic graphs
We study a simple geometric model for local transformations of bipartite graphs. The state consists of a choice of a vector at each white vertex made...
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Dynamical Systems with Hydrodynamic Background
This chapter is a survey of several relevant systems to which the grouptheoretic scheme of the preceding chapters or its modifications can be...
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Nineteenth Century
Gaspard Monge (1746–1818) Monge, G. led a revival of geometry in France. Despite his background as a commoner, his talent brought him in 1765 to...
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Golden GCR-Lightlike Submanifolds of Golden Semi-Riemannian Manifolds
We introduce golden GCR-lightlike submanifolds of golden semi-Riemannian manifolds. We investigate several properties of such submanifolds. Moreover,...
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Building New Einstein Spaces by Deforming Symmetric Einstein Spaces
We introduce an approach to determine new pseudo-Riemannian Einstein spaces by deforming symmetric pseudo-Riemannian Einstein spaces. The metrics of...
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An encounter of classical differential geometry with dynamical systems in the realm of structural stability of principal curvature configurations
This evocative essay focuses on some landmarks that led the author to the study of principal curvature configurations on surfaces in
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Self-Similar Groups and Holomorphic Dynamics: Renormalization, Integrability, and Spectrum
In this paper, we explore the spectral measures of the Laplacian on Schreier graphs for several self-similar groups (the Grigorchuk, Lamplighter, and...
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Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis
Advancements in manufacturing technology, including the rapid development of additive manufacturing (AM), allow the fabrication of complex...