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1 Annales Polonici Mathematici

3 Opozda B.

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Metric polynomial structures

100%

Opozda B.

Instytut Matematyczny Polskiej Akademii Nauk

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

Some contributions to the differential geometry of submanifolds

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Opozda B.

Instytut Matematyczny Polskiej Akademii Nauk

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

Generic submanifolds in almost Hermitian manifolds

41%

Opozda B.

nr 2

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