Basic concepts of the theory of geometric objects

M. Kucharzewski; M. Kuczma

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1964

Abstract

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ContentsIntroduction............................................................................................................................................................................... 3§ 1. Historical development of the concept of a geometric object..................................................................................4§ 2. Manifold, coordinate system, transformations of the coordinate system............................................................. 7§ 3. Group, pseudogroup, groupoid.................................................................................................................................... 9§ 4. Wundheiler's definition of a geometric object........................................................................................................... 15§ 5. Special geometric objects............................................................................................................................................. 18§ 6. Abstract geometric object. The Haantjes-Laman definition of a geometric object............................................. 24§ 7. Classification of geometric objects.............................................................................................................................. 28§ 8. Equivalence of geometric objects................................................................................................................................ 39§ 9. Fibres of equivalent geometric objects....................................................................................................................... 42§ 10. Concomitants................................................................................................................................................................. 47§ 11. Algebra of geometric objects...................................................................................................................................... 54§ 12. Differential concomitants............................................................................................................................................. 57References............................................................................................................................................................................... 63

How to cite

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M. Kucharzewski, and M. Kuczma. Basic concepts of the theory of geometric objects. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1964. <http://eudml.org/doc/268445>.

@book{M1964,
abstract = {ContentsIntroduction............................................................................................................................................................................... 3§ 1. Historical development of the concept of a geometric object..................................................................................4§ 2. Manifold, coordinate system, transformations of the coordinate system............................................................. 7§ 3. Group, pseudogroup, groupoid.................................................................................................................................... 9§ 4. Wundheiler's definition of a geometric object........................................................................................................... 15§ 5. Special geometric objects............................................................................................................................................. 18§ 6. Abstract geometric object. The Haantjes-Laman definition of a geometric object............................................. 24§ 7. Classification of geometric objects.............................................................................................................................. 28§ 8. Equivalence of geometric objects................................................................................................................................ 39§ 9. Fibres of equivalent geometric objects....................................................................................................................... 42§ 10. Concomitants................................................................................................................................................................. 47§ 11. Algebra of geometric objects...................................................................................................................................... 54§ 12. Differential concomitants............................................................................................................................................. 57References............................................................................................................................................................................... 63},
author = {M. Kucharzewski, M. Kuczma},
keywords = {vector and tensor calculus},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Basic concepts of the theory of geometric objects},
url = {http://eudml.org/doc/268445},
year = {1964},
}

TY - BOOK
AU - M. Kucharzewski
AU - M. Kuczma
TI - Basic concepts of the theory of geometric objects
PY - 1964
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - ContentsIntroduction............................................................................................................................................................................... 3§ 1. Historical development of the concept of a geometric object..................................................................................4§ 2. Manifold, coordinate system, transformations of the coordinate system............................................................. 7§ 3. Group, pseudogroup, groupoid.................................................................................................................................... 9§ 4. Wundheiler's definition of a geometric object........................................................................................................... 15§ 5. Special geometric objects............................................................................................................................................. 18§ 6. Abstract geometric object. The Haantjes-Laman definition of a geometric object............................................. 24§ 7. Classification of geometric objects.............................................................................................................................. 28§ 8. Equivalence of geometric objects................................................................................................................................ 39§ 9. Fibres of equivalent geometric objects....................................................................................................................... 42§ 10. Concomitants................................................................................................................................................................. 47§ 11. Algebra of geometric objects...................................................................................................................................... 54§ 12. Differential concomitants............................................................................................................................................. 57References............................................................................................................................................................................... 63
LA - eng
KW - vector and tensor calculus
UR - http://eudml.org/doc/268445
ER -

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