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Some contributions to the differential geometry of submanifolds

100%
Opozda B.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS I. 1. Introduction..................................................................................................................................................................5    2. Preliminaries..............................................................................................................................................................11    3. On Simon’s conjecture..............................................................................................................................................13 II. Pinching theorems for submanifolds of the nearly Kähler 6-sphere..............................................................................16    1. The nearly Kähler structure on S⁶(1)........................................................................................................................16    2. 3-dimensional totally real submanifolds of S⁶............................................................................................................18    3. Totally real surfaces in S⁶..........................................................................................................................................27 III. Surfaces in complex and Sasakian space forms with parallel mean curvature vector...................................................31    1. Totally real surfaces in Kähler manifolds...................................................................................................................31    2. Surfaces of genus 0 with parallel mean curvature vector..........................................................................................34    3. Reduction theorems..................................................................................................................................................51    4. Surfaces of genus 0, C-totally real immersed in Sasakian space forms with parallel mean curvature vector............56 References......................................................................................................................................................................63
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Metric polynomial structures

100%
Opozda B.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Introduction.................................................................................................................................................5 1. Preliminaries...........................................................................................................................................6 2. f-Kählerian manifolds............................................................................................................................11 3. The f-sectional curvature of f-Kählerian manifolds...............................................................................20 4. Complete f-Kählerian manifolds............................................................................................................27 5. Cosymplectic structures. Structures induced on submanifolds of Kählerian manifolds.........................34 References...............................................................................................................................................45
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Parallel hypersurfaces

61%
Opozda B., Simon U.
Annales Polonici Mathematici
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2014
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tom 111
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nr 2
107-135
EN
We investigate parallel hypersurfaces in the context of relative hypersurface geometry, in particular including the cases of Euclidean and Blaschke hypersurfaces. We describe the geometric relations between parallel hypersurfaces in terms of deformation operators, and we apply the results to the parallel deformation of special classes of hypersurfaces, e.g. quadrics and Weingarten hypersurfaces.
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Hypersurfaces with parallel affine curvature tensor R*

61%
Opozda B., Verstraelen L.
Annales Polonici Mathematici
|
1999
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tom 72
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nr 1
25-32
EN
In [OV] we introduced an affine curvature tensor R*. Using it we characterized some types of hypersurfaces in the affine space $ℝ^{n+1}$. In this paper we study hypersurfaces for which R* is parallel relative to the induced connection.
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A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach

49%
Kowalski O., Opozda B., Vlášek Z.
Open Mathematics
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2004
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tom 2
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nr 1
87-102
EN
The aim of this paper is to classify (lócally) all torsion-less locally homogeneous affine connections on two-dimensional manifolds from a group-theoretical point of view. For this purpose, we are using the classification of all non-equivalent transitive Lie algebras of vector fields in ℝ2 according to P.J. Olver [7].
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Curvature homogeneity of affine connections on two-dimensional manifolds

49%
Kowalski O., Opozda B., Vlášek Z.
Colloquium Mathematicum
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1999
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tom 81
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nr 1
123-139
EN
Curvature homogeneity of (torsion-free) affine connections on manifolds is an adaptation of a concept introduced by I. M. Singer. We analyze completely the relationship between curvature homogeneity of higher order and local homogeneity on two-dimensional manifolds.
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On totally umbilical submanifolds in nearly Kählerian manifolds

48%
Opozda B.
Annales Polonici Mathematici
|
1988-1989
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tom 49
|
nr 3
221-227
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The f-sectional curvature of f-Kaehlerian manifolds

42%
Opozda B.
Annales Polonici Mathematici
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1983
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tom 43
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nr 2
141-150
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Generic submanifolds in almost Hermitian manifolds

42%
Opozda B.
Annales Polonici Mathematici
|
1988-1989
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tom 49
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nr 2
115-128
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