Ebook: Riemanns geometrische Ideen, ihre Auswirkung und ihre Verknüpfung mit der Gruppentheorie

Ganz in Hermann Weyls bekannt klarer Darstellung geschrieben, gibt dieser Beitrag einen Bericht über die Entstehung der grundlegenden Ideen, die der modernen Geometrie zugrunde liegen. Diese Schrift spiegelt in einzigartiger Weise Weyls mathematische Persönlichkeit wider. Sie richtet sich an alle, die sich mit Fragen der Topologiegruppentheorie, Differentialgeometrie und mathematischer Physik beschäftigen. From the foreword of theeditor K. Chandrasekharan: "Written in Weyl's finest style, while he was rising forty, the article is an authentic report on the genesis and evolution of those fundamental ideas that underlie the modern conception of geometry. Part I is on the continuum, and deals with analysis situs, imbeddings, and coverings. Part II is on structure, and deals with infinitesimal geometry in its many aspects, metric, conformal, affine, and projective; with the question of homogeneity, homogeneous spaces from the group-theoretical standpoint, the role of the metric field theories in physics, and the related problems of group theory. It is hoped that this article will be of interest to all those concerned with the growth and development of topology, group theory, differential geometry, geometric function theory, and mathematical physics. It bears the unmistakable imprint of Weyl's mathematical personality, and of his remarkable capacity to capture and delineate the transmutation of some of the nascent into the dominant ideas of the mathematics of our time".

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Ganz in Hermann Weyls bekannt klarer Darstellung geschrieben, gibt dieser Beitrag einen Bericht ?ber die Entstehung der grundlegenden Ideen, die der modernen Geometrie zugrunde liegen. Diese Schrift spiegelt in einzigartiger Weise Weyls mathematische Pers?nlichkeit wider. Sie richtet sich an alle, die sich mit Fragen der Topologiegruppentheorie, Differentialgeometrie und mathematischer Physik besch?ftigen. From the foreword of theeditor K. Chandrasekharan: "Written in Weyl's finest style, while he was rising forty, the article is an authentic report on the genesis and evolution of those fundamental ideas that underlie the modern conception of geometry. Part I is on the continuum, and deals with analysis situs, imbeddings, and coverings. Part II is on structure, and deals with infinitesimal geometry in its many aspects, metric, conformal, affine, and projective; with the question of homogeneity, homogeneous spaces from the group-theoretical standpoint, the role of the metric field theories in physics, and the related problems of group theory. It is hoped that this article will be of interest to all those concerned with the growth and development of topology, group theory, differential geometry, geometric function theory, and mathematical physics. It bears the unmistakable imprint of Weyl's mathematical personality, and of his remarkable capacity to capture and delineate the transmutation of some of the nascent into the dominant ideas of the mathematics of our time".

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Ganz in Hermann Weyls bekannt klarer Darstellung geschrieben, gibt dieser Beitrag einen Bericht ?ber die Entstehung der grundlegenden Ideen, die der modernen Geometrie zugrunde liegen. Diese Schrift spiegelt in einzigartiger Weise Weyls mathematische Pers?nlichkeit wider. Sie richtet sich an alle, die sich mit Fragen der Topologiegruppentheorie, Differentialgeometrie und mathematischer Physik besch?ftigen. From the foreword of theeditor K. Chandrasekharan: "Written in Weyl's finest style, while he was rising forty, the article is an authentic report on the genesis and evolution of those fundamental ideas that underlie the modern conception of geometry. Part I is on the continuum, and deals with analysis situs, imbeddings, and coverings. Part II is on structure, and deals with infinitesimal geometry in its many aspects, metric, conformal, affine, and projective; with the question of homogeneity, homogeneous spaces from the group-theoretical standpoint, the role of the metric field theories in physics, and the related problems of group theory. It is hoped that this article will be of interest to all those concerned with the growth and development of topology, group theory, differential geometry, geometric function theory, and mathematical physics. It bears the unmistakable imprint of Weyl's mathematical personality, and of his remarkable capacity to capture and delineate the transmutation of some of the nascent into the dominant ideas of the mathematics of our time".
Content:
Front Matter....Pages I-1
Begriff der n-dimensionalen Mannigfaltigkeit....Pages 2-12
Analysis situs....Pages 12-17
Einbettung und ?berlagerung....Pages 17-22
Das Strukturfeld ....Pages 23-28
Die Frage der Homogenit?t....Pages 29-31
Der homogene Raum vom gruppentheoretischen Standpunkt....Pages 31-35
Das metrische als physikalisches Zustandsfeld. Das zugeh?rige gruppentheoretische Raumproblem. Cartans Untersuchungen....Pages 36-41
Mathematics and the laws of nature....Pages 43-46

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Ganz in Hermann Weyls bekannt klarer Darstellung geschrieben, gibt dieser Beitrag einen Bericht ?ber die Entstehung der grundlegenden Ideen, die der modernen Geometrie zugrunde liegen. Diese Schrift spiegelt in einzigartiger Weise Weyls mathematische Pers?nlichkeit wider. Sie richtet sich an alle, die sich mit Fragen der Topologiegruppentheorie, Differentialgeometrie und mathematischer Physik besch?ftigen. From the foreword of theeditor K. Chandrasekharan: "Written in Weyl's finest style, while he was rising forty, the article is an authentic report on the genesis and evolution of those fundamental ideas that underlie the modern conception of geometry. Part I is on the continuum, and deals with analysis situs, imbeddings, and coverings. Part II is on structure, and deals with infinitesimal geometry in its many aspects, metric, conformal, affine, and projective; with the question of homogeneity, homogeneous spaces from the group-theoretical standpoint, the role of the metric field theories in physics, and the related problems of group theory. It is hoped that this article will be of interest to all those concerned with the growth and development of topology, group theory, differential geometry, geometric function theory, and mathematical physics. It bears the unmistakable imprint of Weyl's mathematical personality, and of his remarkable capacity to capture and delineate the transmutation of some of the nascent into the dominant ideas of the mathematics of our time".
Content:
Front Matter....Pages I-1
Begriff der n-dimensionalen Mannigfaltigkeit....Pages 2-12
Analysis situs....Pages 12-17
Einbettung und ?berlagerung....Pages 17-22
Das Strukturfeld ....Pages 23-28
Die Frage der Homogenit?t....Pages 29-31
Der homogene Raum vom gruppentheoretischen Standpunkt....Pages 31-35
Das metrische als physikalisches Zustandsfeld. Das zugeh?rige gruppentheoretische Raumproblem. Cartans Untersuchungen....Pages 36-41
Mathematics and the laws of nature....Pages 43-46
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