DIFFERENTIAL GEOMETRY OF THREE DIMENSIONS

By Q. NAORN

CONTENTS PLANE CURVES AND SPACE CURVES CONCEPT OF CURVES PLANE CURVES GLOBAL THEOREMS ON PLANE CURVES SPACE CURVES GLOBAL RESULTS ON SPACE CURVES LOCAL THEORY OF SURFACES IN THE SPACE CONCEPT OF SURFACES IN THE SPACE FUNDAMENTAL FORMS AND CURVATURES EXAMPLES AND CALCULATIONS OF FUNDAMENTAL FORMS AND CURVATURES METHOD OF ORTHONORMAL FRAMES EXTERIOR DI?ERENTIAL FORMS IN TWO VARIABLES USE OF EXTERIOR DI?ERENTIAL FORMS GEOMETRY OF SURFACES RIEMANNIAN METRICS ON A SURFACE STRUCTURE EQUATIONS OF A SURFACE VECTOR FIELDS COVARIANT DERIVATIVES AND PARALLEL TRANSLATIONS GEODESICS GEODESICS AS SHORTEST CURVES THE GAUSS-BONNET THEOREM INTEGRATION OF EXTERIOR DI?ERENTIAL FORMS THE GAUSS-BONNET THEOREM (DOMAINS) THE GAUSS-BONNET THEOREM (CLOSED SURFACES) MINIMAL SURFACES MEAN CURVATURES AND MINIMAL SURFACES EXAMPLES OF MINIMAL SURFACES ISOTHERMAL COORDINATE SYSTEMS THE WEIERSTRASS-ENNEPER REPRESENTATION ASSOCIATED MINIMAL SURFACES CURVATURES OF MINIMAL SURFACES GAUSS’ SPHERICAL MAPS