Saburo IDE Contents \S 0. Introduction. 75 .\S 1. Theory of the WIRTINGER'S connection. 76 \S 2. Generalized WIRTINGER'S connections. 79 \S 3. WIRTINGER'S connections introduced in KAWAGUCHI spacae. 83 \S 4. Covariant derivatives. 93 \S 5. Covariant derivatives in a special KAWAGUCHI space. 96 \S 6. Curvature t\"ensors and identities in a special KAWAGUCHI space. . 108 References.