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Line field

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over the manifold. Line fields are of particular interest in the study of
83: 258:"Line Element Fields and Lorentz Structures on Differentiable Manifolds" 289: 257: 273: 102:, where it is conventional to modify the definition slightly. 18: 192:
In the study of complex dynamical systems, the manifold
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may be too technical for most readers to understand
90:being tangent to a manifold at each point, i.e. a 341: 8: 227:in the general sense above that is defined 145:) through the origin in the tangent space T 348: 334: 62:Learn how and when to remove this message 46:, without removing the technical details. 248: 44:make it understandable to non-experts 7: 302: 300: 155:). Equivalently, one may say that 320:. You can help Knowledge (XXG) by 14: 216:is required to have positive two- 304: 23: 181:is a section of the projective 1: 377:Mathematical analysis stubs 129:that assigns to each point 393: 299: 100:complex dynamical systems 165:projective tangent space 163:) is an element of the 316:–related article is a 314:mathematical analysis 262:Annals of Mathematics 223:) is a line field on 86:is a formation of a 256:Markus, L. (1955). 237:measurable function 114:be a manifold. A 367:Dynamical systems 329: 328: 229:almost everywhere 196:is taken to be a 72: 71: 64: 384: 350: 343: 336: 308: 301: 294: 293: 253: 221:Lebesgue measure 110:In general, let 67: 60: 56: 53: 47: 27: 26: 19: 392: 391: 387: 386: 385: 383: 382: 381: 357: 356: 355: 354: 298: 297: 274:10.2307/1970071 255: 254: 250: 245: 172: 150: 108: 68: 57: 51: 48: 40:help improve it 37: 28: 24: 17: 12: 11: 5: 390: 388: 380: 379: 374: 369: 359: 358: 353: 352: 345: 338: 330: 327: 326: 309: 296: 295: 268:(3): 411–417. 247: 246: 244: 241: 235:and is also a 198:Hersee surface 183:tangent bundle 168: 146: 107: 104: 70: 69: 31: 29: 22: 15: 13: 10: 9: 6: 4: 3: 2: 389: 378: 375: 373: 372:Fiber bundles 370: 368: 365: 364: 362: 351: 346: 344: 339: 337: 332: 331: 325: 323: 319: 315: 310: 307: 303: 291: 287: 283: 279: 275: 271: 267: 263: 259: 252: 249: 242: 240: 238: 234: 230: 226: 222: 219: 215: 211: 207: 203: 199: 195: 190: 188: 184: 180: 176: 171: 166: 162: 158: 154: 149: 144: 140: 136: 132: 128: 125: 121: 117: 113: 105: 103: 101: 97: 93: 89: 85: 81: 77: 66: 63: 55: 45: 41: 35: 32:This article 30: 21: 20: 322:expanding it 311: 265: 261: 251: 232: 224: 213: 209: 205: 204:on a subset 201: 193: 191: 186: 178: 174: 169: 160: 156: 152: 147: 142: 138: 134: 130: 126: 119: 115: 111: 109: 79: 73: 58: 49: 33: 218:dimensional 177:), or that 106:Definitions 96:line bundle 76:mathematics 361:Categories 243:References 202:line field 116:line field 80:line field 52:April 2024 16:Math topic 282:0003-486X 124:function 84:manifold 290:1970071 212:(where 137:a line 94:of the 92:section 38:Please 288:  280:  312:This 286:JSTOR 200:. A 122:is a 82:on a 318:stub 278:ISSN 88:line 78:, a 270:doi 231:in 208:of 189:). 185:PT( 133:of 118:on 74:In 42:to 363:: 284:. 276:. 266:62 264:. 260:. 239:. 167:PT 349:e 342:t 335:v 324:. 292:. 272:: 233:A 225:A 214:A 210:M 206:A 194:M 187:M 179:μ 175:M 173:( 170:p 161:p 159:( 157:μ 153:M 151:( 148:p 143:p 141:( 139:μ 135:M 131:p 127:μ 120:M 112:M 65:) 59:( 54:) 50:( 36:.

Index

help improve it
make it understandable to non-experts
Learn how and when to remove this message
mathematics
manifold
line
section
line bundle
complex dynamical systems
function
projective tangent space
tangent bundle
Hersee surface
dimensional
Lebesgue measure
almost everywhere
measurable function
"Line Element Fields and Lorentz Structures on Differentiable Manifolds"
doi
10.2307/1970071
ISSN
0003-486X
JSTOR
1970071
Stub icon
mathematical analysis
stub
expanding it
v
t

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