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Chen-Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds

Erol Kılıç, Mukut Mani Tripathi, Mehmet Gülbahar (2016)

Annales Polonici Mathematici

Some examples of slant submanifolds of almost product Riemannian manifolds are presented. The existence of a useful orthonormal basis in proper slant submanifolds of a Riemannian product manifold is proved. The sectional curvature, the Ricci curvature and the scalar curvature of submanifolds of locally product manifolds of almost constant curvature are obtained. Chen-Ricci inequalities involving the Ricci tensor and the squared mean curvature for submanifolds of locally product manifolds of almost...

Chen's inequality in the Lagrangian case

Teodor Oprea (2007)

Colloquium Mathematicae

In the theory of submanifolds, the following problem is fundamental: establish simple relationships between the main intrinsic invariants and the main extrinsic invariants of submanifolds. The basic relationships discovered until now are inequalities. To analyze such problems, we follow the idea of C. Udrişte that the method of constrained extremum is a natural way to prove geometric inequalities. We improve Chen's inequality which characterizes a totally real submanifold of a complex space form....

Chern classes of vector bundles with singular connections

Guiseppe De Cecco (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si fa vedere che alcune classi di Chern di fibrati vettoriali complessi possono essere costruite non solo partendo da connessioni C ∞ ma, sotto certe condizioni, anche da connessioni lineari singolari. Nel caso particolare del fibrato tangente possono essere costruite anche a partire da metriche singolari. Viene fatto uso in modo essenziale della L 2 -coomologia di de Rham (introdotta da Cheeger e Teleman).

Circular cone and its Gauss map

Miekyung Choi, Dong-Soo Kim, Young Ho Kim, Dae Won Yoon (2012)

Colloquium Mathematicae

The family of cones is one of typical models of non-cylindrical ruled surfaces. Among them, the circular cones are unique in the sense that their Gauss map satisfies a partial differential equation similar, though not identical, to one characterizing the so-called 1-type submanifolds. Specifically, for the Gauss map G of a circular cone, one has ΔG = f(G+C), where Δ is the Laplacian operator, f is a non-zero function and C is a constant vector. We prove that circular cones are characterized by being...

Circular vectors and toroidal matrices

Znojil, M. (1996)

Proceedings of the Winter School "Geometry and Physics"

Summary: Arrays of numbers may be written not only on a line (= ``a vector'') or in the plain (= ``a matrix'') but also on a circle (= ``a circular vector''), on a torus (= ``a toroidal matrix'') etc. In the latter case, the immanent index-rotation ambiguity converts the standard ``scalar'' product into a binary operation with several interesting properties.

Circuminscribed polygons in a plane annulus

Waldemar Cieślak, Elżbieta Szczygielska (2008)

Annales UMCS, Mathematica

Each oval and a natural number n ≥ 3 generate an annulus which possesses the Poncelet's porism property. A necessary and sufficient condition of existence of circuminscribed n-gons in an annulus is given.

Classes caractéristiques exotiques et ℐ -connexité des espaces de connexions

Daniel Lehmann (1974)

Annales de l'institut Fourier

Le but de ce travail est double : d’une part, généraliser la construction des classes exotiques pour l’appliquer à d’autres problèmes géométriques que ceux issus des Γ -structures ; d’autre part, préciser, grâce à la notion de J -connexité, remplaçant avantageusement les formules de dérivation utilisées précédemment, l’argument d’invariance homotopique permettant d’obtenir des théorèmes de rigidité, montrant simultanément pourquoi la seule connexité des ensembles de connexions considérés ne suffit...

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