FOLIATIONS AND GEOMETRIC STRUCTURES

By I. LUSIA

CONTENTS GEOMETRY OF DISTRIBUTIONS ON A MANIFOLD DISTRIBUTIONS ON A MANIFOLD ADAPTED LINEAR CONNECTIONS ON ALMOST PRODUCT MANIFOLDS THE SCHOUTEN–VAN KAMPEN AND VR?ANCEANU CONNECTIONS FROM SEMI–EUCLIDEAN ALGEBRA TO SEMI–RIEMANNIAN GEOMETRY INTRINSIC AND INDUCED LINEAR CONNECTIONS ON SEMI– RIEMANNIAN DISTRIBUTIONS FUNDAMENTAL EQUATIONS FOR SEMI–RIEMANNIAN DISTRIBUTIONS SECTIONAL CURVATURES OF A SEMI–RIEMANNIAN NON–HOLONOMIC MANIFOLD DEGENERATE DISTRIBUTIONS OF CODIMENSION ONE STRUCTURAL AND TRANSVERSAL GEOMETRY OF FOLIATIONS DE?NITIONS AND EXAMPLES ADAPTED TENSOR FIELDS ON A FOLIATED MANIFOLD STRUCTURAL AND TRANSVERSAL LINEAR CONNECTIONS RICCI AND BIANCHI IDENTITIES FOLIATIONS ON SEMI–RIEMANNIAN MANIFOLDS THE VR?ANCEANU CONNECTION ON A FOLIATED SEMI–RIEMANNIAN MANIFOLD THE SCHOUTEN–VAN KAMPEN CONNECTION ON A FOLIATED SEMI–RIEMANNIAN MANIFOLD SPECIAL CLASSES OF FOLIATIONS TOTALLY GEODESIC FOLIATIONS ON SEMI–RIEMANNIAN MANIFOLDS TOTALLY UMBILICAL FOLIATIONS ON SEMI–RIEMANNIAN MANIFOLDS MINIMAL FOLIATIONS ON RIEMANNIAN MANIFOLDS DEGENERATE FOLIATIONS OF CODIMENSION ONE PARALLEL FOLIATIONS PARALLELISM PARALLELISM ON ALMOST PRODUCT MANIFOLDS PARALLELISM ON SEMI–RIEMANNIAN MANIFOLDS PARALLEL NON–DEGENERATE FOLIATIONS PARALLEL TOTALLY–NULL FOLIATIONS PARALLEL TOTALLY–NULL R–FOLIATIONS ON 2R–DIMENSIONAL SEMI–RIEMANNIAN MANIFOLDS PARALLEL PARTIALLY–NULL FOLIATIONS MANIFOLDS WITH WALKER COMPLEMENTARY FOLIATIONS PARALLEL FOLIATIONS AND G–STRUCTURES FOLIATIONS INDUCED BY GEOMETRIC STRUCTURES LAGRANGE FOLIATIONS ON SYMPLECTIC MANIFOLDS LEGENDRE FOLIATIONS ON CONTACT MANIFOLDS FOLIATIONS ON THE TANGENT BUNDLE OF A FINSLER MANIFOLD FOLIATIONS ON CR-SUBMANIFOLDS A GAUGE THEORY ON A VECTOR BUNDLE ADAPTED TENSOR FIELDS ON THE TOTAL SPACE OF A VECTOR BUNDLE GLOBAL GAUGE INVARIANCE OF LAGRANGIANS ON A VECTOR BUNDLE LOCAL GAUGE INVARIANCE ON A VECTOR BUNDLE EQUATIONS OF MOTION AND CONSERVATION LAWS BIANCHI IDENTITIES FOR STRENGTH FIELDS