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Coordinate-induced basis

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that is induced by a certain coordinate system. Given the coordinate system
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Topics in Differential Geometry: a New Approach Using D-Differentiation
15: 240:{\displaystyle e_{a}={\frac {\partial }{\partial x^{a}}}} 368: 286: 256: 201: 171: 144: 46:. Unsourced material may be challenged and removed. 319: 269: 239: 184: 157: 388: 8: 395: 381: 316: 307: 291: 285: 261: 255: 228: 215: 206: 200: 176: 170: 149: 143: 106:Learn how and when to remove this message 320:{\displaystyle \omega ^{a}=dx^{a}.\,} 7: 349: 347: 44:adding citations to reliable sources 221: 217: 192:of the tangent space is given by 14: 351: 20: 165:, the coordinate-induced basis 31:needs additional citations for 1: 367:. You can help Knowledge by 419:Differential geometry stubs 277:of the cotangent space is 270:{\displaystyle \omega ^{a}} 435: 346: 336:D.J. Hurley, M.A. Vandyck 55:"Coordinate-induced basis" 340:(2002 Springer) p. 5 124:coordinate-induced basis 363:-related article is a 321: 271: 241: 186: 159: 414:Differential geometry 361:differential geometry 322: 272: 242: 187: 185:{\displaystyle e_{a}} 160: 158:{\displaystyle x^{a}} 284: 254: 199: 169: 142: 40:improve this article 250:and the dual basis 126:is a basis for the 317: 267: 237: 182: 155: 376: 375: 235: 116: 115: 108: 90: 426: 397: 390: 383: 355: 348: 326: 324: 323: 318: 312: 311: 296: 295: 276: 274: 273: 268: 266: 265: 246: 244: 243: 238: 236: 234: 233: 232: 216: 211: 210: 191: 189: 188: 183: 181: 180: 164: 162: 161: 156: 154: 153: 111: 104: 100: 97: 91: 89: 48: 24: 16: 434: 433: 429: 428: 427: 425: 424: 423: 404: 403: 402: 401: 344: 333: 303: 287: 282: 281: 257: 252: 251: 224: 220: 202: 197: 196: 172: 167: 166: 145: 140: 139: 132:cotangent space 112: 101: 95: 92: 49: 47: 37: 25: 12: 11: 5: 432: 430: 422: 421: 416: 406: 405: 400: 399: 392: 385: 377: 374: 373: 356: 342: 341: 332: 329: 328: 327: 315: 310: 306: 302: 299: 294: 290: 264: 260: 248: 247: 231: 227: 223: 219: 214: 209: 205: 179: 175: 152: 148: 114: 113: 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 431: 420: 417: 415: 412: 411: 409: 398: 393: 391: 386: 384: 379: 378: 372: 370: 366: 362: 357: 354: 350: 345: 339: 335: 334: 330: 313: 308: 304: 300: 297: 292: 288: 280: 279: 278: 262: 258: 229: 225: 212: 207: 203: 195: 194: 193: 177: 173: 150: 146: 137: 133: 129: 128:tangent space 125: 121: 110: 107: 99: 88: 85: 81: 78: 74: 71: 67: 64: 60: 57: –  56: 52: 51:Find sources: 45: 41: 35: 34: 29:This article 27: 23: 18: 17: 369:expanding it 358: 343: 337: 249: 123: 117: 102: 96:January 2010 93: 83: 76: 69: 62: 50: 38:Please help 33:verification 30: 120:mathematics 408:Categories 331:References 66:newspapers 289:ω 259:ω 222:∂ 218:∂ 136:manifold 80:scholar 82:  75:  68:  61:  53:  359:This 134:of a 87:JSTOR 73:books 365:stub 122:, a 59:news 130:or 118:In 42:by 410:: 396:e 389:t 382:v 371:. 314:. 309:a 305:x 301:d 298:= 293:a 263:a 230:a 226:x 213:= 208:a 204:e 178:a 174:e 151:a 147:x 109:) 103:( 98:) 94:( 84:· 77:· 70:· 63:· 36:.

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