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Framed slant helices in Euclidean 3-space
In this paper, we define framed slant helices and give a necessary and sufficient condition for them in three-dimensional Euclidean space. Then, we...
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Spectral dimension, Euclidean embeddings, and the metric growth exponent
For reversible random networks, we exhibit a relationship between the almost sure spectral dimension and the Euclidean growth exponent, which is the...
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A Class of Einstein Submanifolds of Euclidean Space
In this paper we give local and global parametric classifications of a class of Einstein submanifolds of Euclidean space. The highlight is for...
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Lectures on Euclidean Geometry - Volume 2 Circle measurement, Transformations, Space Geometry, Conics
This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume...
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Ricci Soliton Biharmonic Hypersurfaces in the Euclidean Space
We investigate biharmonic Ricci soliton hypersurfaces ( M n , g, 𝜉 , ⋋ ) whose potential field 𝜉 satisfies certain conditions. We obtain a result based...
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Lectures on Euclidean Geometry - Volume 1 Euclidean Geometry of the Plane
This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume...
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Singularities of Translation Surfaces in the Euclidean 3-Space
We study on singular points of translation surfaces in the Euclidean 3-space by using the theory of framed curves and framed surfaces. We introduce...
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Sharp upper bounds for Steklov eigenvalues of a hypersurface of revolution with two boundary components in Euclidean space
We investigate the question of sharp upper bounds for the Steklov eigenvalues of a hypersurface of revolution in Euclidean space with two boundary...
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Generalized Yamabe solitons on hypersurfaces in pseudo–Euclidean spaces
In this paper, we obtain a classification theorem for generalized Yamabe solitons, called conformal solitons, on pseudo–Riemannian hypersurfaces in...
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Pythagorean Submanifolds in Euclidean Spaces
In this paper we introduce the notion of a Pythagorean submanifold isometrically immersed into a Euclidean space. This definiton will be based on the...
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Distributions in Euclidean Space
In the first section of this chapterwe transition from functions to generalized functions of the most commonly used kind, the distributions in an...
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Hyperfunctions in Euclidean Space
Hyperfunctions are defined in real space \( \mathbb{R}^{n} \) ,...
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Euclidean and Non-Euclidean Geometry in the History and Philosophy of Mathematical Practice
In the history of mathematical practice, geometry serves as an important focal point through which numerous changes in practice and associated...
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Linked partition ideals and Euclidean billiard partitions
Euclidean billiard partitions were recently introduced by Andrews, Dragović and Radnović in their study of periodic trajectories of ellipsoidal...
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Elastic Metrics on Spaces of Euclidean Curves: Theory and Algorithms
A main goal in the field of statistical shape analysis is to define computable and informative metrics on spaces of immersed manifolds, such as the...
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On the Curvatures of a Curve in n-Dimensional Euclidean Space
Formulas are obtained for calculating the curvatures of an implicitly defined curve in n -dimensional Euclidean space. For these curves, Beltrami's...
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The Euclidean Ball—The Drury Arveson Space
This chapter treats a commuting contractive tuple from the function theoretic point of view. This means introducing the Drury-Arveson space and...