(Ebook) A Treatise on the Differential Geometry of Curves and Surfaces Dover Phoenix Editions 1st edition by Luther Pfahler Eisenhart 0486438201 9780486438207

(Ebook) A Treatise on the Differential Geometry of Curves and Surfaces Dover Phoenix Editions 1st edition by Luther Pfahler Eisenhart 0486438201 9780486438207

A Treatise on the Differential Geometry of Curves and Surfaces (Dover Phoenix Editions) 1st edition by Luther Pfahler Eisenhart - Ebook PDF Instant Download/DeliveryISBN: 0486438201, 9780486438207 

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ISBN-10 :  0486438201 

ISBN-13 :  9780486438207

Author:  Luther Pfahler Eisenhart  

Created especially for graduate students, this introductory treatise on differential geometry has been a highly successful textbook for many years. Its unusually detailed and concrete approach includes a thorough explanation of the geometry of curves and surfaces, concentrating on problems that will be most helpful to students. 1909 edition.

A Treatise on the Differential Geometry of Curves and Surfaces (Dover Phoenix Editions) 1st Table of contents:

CHAPTER I

PARAMETRIC EQUATIONS OF A CURVE
OTHER FORMS OF THE EQUATIONS OF A CURVE
LINEAR ELEMENT
TANGENT TO A CURVE
ORDER OF CONTACT NORMAL PLANE
CURVATURE RADIUS OF FIRST CURVATURE
OSCULATING PLANE
PRINCIPAL NORMAL AND BINORMAL
LINE OF STRICTION DEVELOPABLE SURFACES
CENTRAL PLANE PARAMETER OF DISTRIBUTION
PARTICULAR FORM OF THE LINEAR ELEMENT
ASYMPTOTIC LINES ORTHOGONAL PARAMETRIC SYSTEMS
MINIMAL SURFACES
LINES OF CURVATURE AND ASYMPTOTIC LINES ADJOINT MINI MAL SURFACES
MINIMAL CURVES ON A MINIMAL SURFACE
DOUBLE MINIMAL SURFACES

OSCULATING CIRCLE CENTER OF FIRST CURVATURE
TORSION FRENETSERRET FORMULAS
FORM OF CURVE IN THE NEIGHBORHOOD OF A POINT THE SIGN OF TORSION
CYLINDRICAL HELICES
INTRINSIC EQUATIONS FUNDAMENTAL THEOREM
RICCATI EQUATIONS
THE DETERMINATION OF THE COÖRDINATES OF A CURVE DEFINED BY ITS INTRINSIC EQUATIONS
MOVING TRIHEDRAL
ILLUSTRATIVE EXAMPLES
OSCULATING SPHERE
BERTRAND CURVES
TANGENT SURFACE OF A CURVE
INVOLUTES AND EVOLUTES OF A CURVE
MINIMAL CURVES
CHAPTER II
PARAMETRIC CURVES
TANGENT PLANE
ONEPARAMETER FAMILIES OF SURFACES ENVELOPES
ENVELOPE OF SPHERES CANAL SURFACES
ISOTROPIC DEVELOPABLE
FAMILIES OF CURVES
DIFFERENTIAL PARAMETERS OF THE SECOND ORDER
ISOTHERMIC ORTHOGONAL SYSTEMS
CONFORMAL REPRESENTATION OF A SURFACE UPON ITSELF
SURFACES OF REVOLUTION
CHAPTER IV
LINES OF CURVATURE EQUATIONS OF RODRIGUES
ASYMPTOTIC LINES CHARACTERISTIC LINES
GEODESIC TORSION
SPHERICAL REPRESENTATION
RELATIONS BETWEEN A SURFACE AND ITS SPHERICAL REPRE SENTATION
HELICOIDS
CHAPTER V
THE EQUATIONS OF GAUSS AND OF CODAZZI
FUNDAMENTAL THEOREM
FUNDAMENTAL EQUATIONS IN ANOTHER FORM
TANGENTIAL COÖRDINATES MEAN EVOLUTE
THE MOVING TRIHEDRAL
FUNDAMENTAL EQUATIONS OF CONDITION
LINEAR ELEMENT LINES OF CURVATURE
CONJUGATE DIRECTIONS AND ASYMPTOTIC DIRECTONS SPHER ICAL REPRESENTATION
FUNDAMENTAL RELATIONS AND FORMULAS
PARALLEL SURFACES
SURFACES OF CENTER
FUNDAMENTAL QUANTITIES FOR SURFACES OF CENTER
SURFACES COMPLEMENTARY TO A GIVEN SURFACE
CHAPTER VI
SPHERICAL REPRESENTATION OF ASYMPTOTIC LINES
FORMULAS OF LELIEUVRE TANGENTIAL EQUATIONS
CONJUGATE SYSTEMS OF PARAMETRIC LINES INVERSIONS
SURFACES OF TRANSLATION
ISOTHERMALCONJUGATE SYSTEMS
SPHERICAL REPRESENTATION OF CONJUGATE SYSTEMS
TANGENTIAL COÖRDINATES PROJECTIVE TRANSFORMATIONS
EQUATIONS OF GEODESIC LINES
GEODESIC PARALLELS GEODESIC PARAMETERS
GEODESIC POLAR COÖRDINATES
AREA OF A GEODESIC TRIANGLE
LINES OF SHORTEST LENGTH GEODESIC CURVATURE
GEODESIC ELLIPSES AND HYPERBOLAS
SURFACES OF LIOUVILLE
INTEGRATION OF THE EQUATION OF GEODESIC LINES
GEODESICS ON SURFACES OF LIOUVILLE
LINES OF SHORTEST LENGTH ENVELOPE OF GEODESICS
CHAPTER VII
FUNDAMENTAL QUANTITIES FOR CENTRAL QUADRICS
FUNDAMENTAL QUANTITIES FOR THE PARABOLOIDS
LINES OF CURVATURE AND ASYMPTOTIC LINES ON QUADRICS
GEODESICS ON QUADRICS
GEODESICS THROUGH THE UMBILICAL POINTS
PROPERTIES OF QUADRICS
EQUATIONS OF A RULED SURFACE
ALGEBRAIC MINIMAL SURFACES
ASSOCIATE SURFACES
FORMULAS OF SCHWARZ
CHAPTER VIII
PSEUDOSPHERICAL SURFACES OF REVOLUTION
GEODESIC PARAMETRIC SYSTEMS APPLICABILITY
TRANSFORMATION OF HAZZIDAKIS
TRANSFORMATION OF BIANCHI
TRANSFORMATION OF BÄCKLUND
THEOREM OF PERMUTABILITY
TRANSFORMATION OF LIE
WSURFACES FUNDAMENTAL QUANTITIES
EVOLUTE OF A WSURFACE
SURFACES OF CONSTANT MEAN CURVATURE
RULED WSURFACES
SPHERICAL REPRESENTATION OF SURFACES WITH PLANE LINES OF CURVATURE IN BOTH SYSTEMS
SURFACES WITH PLANE LINES OF CURVATURE IN BOTH SYSTEMS
SURFACES WITH PLANE LINES OF CURVATURE IN ONE SYSTEM SURFACES OF MONGE
MOLDING SURFACES
SURFACES OF JOACHIMSTHAL
SURFACES WITH CIRCULAR LINES OF CURVATURE
CYCLIDES OF DUPIN
SURFACES WITH SPHERICAL LINES OF CURVATURE IN ONE SYSTEM
CHAPTER IX
SOLUTION OF THE PROBLEM OF MINDING
DEFORMATION OF MINIMAL SURFACES
SECOND GENERAL PROBLEM OF DEFORMATION
DEFORMATIONS WHICH CHANGE A CURVE ON THE SURFACE INTO A GIVEN CURVE IN SPACE
LINES OF CURVATURE IN CORRESPONDENCE
CONJUGATE SYSTEMS IN CORRESPONDENCE
ASYMPTOTIC LINES IN CORRESPONDENCE DEFORMATION OF A RULED SURFACE
МЕТHOD OF MINDING
PARTICULAR DEFORMATIONS OF RULED SURFACES
CHAPTER X
GENERAL FORMULAS
THE THEOREM OF WEINGARTEN
OTHER FORMS OF THE THEOREM OF WEINGARTEN
SURFACES APPLICABLE TO A SURFACE OF REVOLUTION
MINIMAL LINES ON THE SPHERE PARAMETRIC
SURFACES OF GOURSAT SURFACES APPLICABLE TO CERTAIN PARABOLOIDS
CHAPTER XI
CHARACTERISTIC FUNCTION
ASYMPTOTIC LINES PARAMETRIC
ASSOCIATE SURFACES
PARTICULAR PARAMETRIC CURVES
RELATIONS BETWEEN THREE SURFACES S S₁ So
SURFACES RESULTING FROM AN INFINITESIMAL DEFORMATION
ISOTHERMIC SURFACES
CHAPTER XII
NORMAL CONGRUENCES RULED SURFACES OF A CONGRUENCE
LIMIT POINTS PRINCIPAL SURFACES
DEVELOPABLE SURFACES OF A CONGRUENCE FOCAL SURFACES
ASSOCIATE NORMAL CONGRUENCES
DERIVED CONGRUENCES
FUNDAMENTAL EQUATIONS OF CONDITION
SPHERICAL REPRESENTATION OF PRINCIPAL SURFACES AND OF DEVELOPABLES
FUNDAMENTAL QUANTITIES FOR THE FOCAL SURFACES
ISOTROPIC CONGRUENCES
CONGRUENCES OF GUICHARD
PSEUDOSPHERICAL CONGRUENCES
WCONGRUENCES
CONGRUENCES OF RIBAUCOUR
CHAPTER XIII
CYCLIC CONGRUENCES
SPHERICAL REPRESENTATION OF CYCLIC CONGRUENCES
CYCLIC SYSTEMS FOR WHICH THE ENVELOPE OF THE PLANES
CHAPTER XIV
TRIPLE SYSTEMS OF BIANCHI AND OF WEINGARTEN
THEOREMS OF DARBOUX
INDEX

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Tags: A Treatise, the Differential Geometry, Curves, Surfaces, Dover Phoenix, Luther Pfahler Eisenhart